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Books > Science & Mathematics > Mathematics > Optimization > General

Exact and Heuristic Methods in Combinatorial Optimization - A Study on the Linear Ordering and the Maximum Diversity Problem... Exact and Heuristic Methods in Combinatorial Optimization - A Study on the Linear Ordering and the Maximum Diversity Problem (Hardcover, 2nd ed. 2022)
Rafael Marti, Gerhard Reinelt
R3,380 Discovery Miles 33 800 Ships in 10 - 15 working days

In the last decades, algorithmic advances as well as hardware and software improvements have provided an excellent environment to create and develop solving methods to hard optimization problems. Modern exact and heuristic techniques are dramatically enhancing our ability to solve significant practical problems. This monograph sets out state-of-the-art methodologies for solving combinatorial optimization problems, illustrating them with two well-known problems. This second edition of the book extends the first one by adding to the 'linear ordering problem' (LOP), included in the first edition, the 'maximum diversity problem' (MDP). In this way, we provide the reader with the background, elements and strategies to tackle a wide range of different combinatorial optimization problems. The exact and heuristic techniques outlined in these pages can be put to use in any number of combinatorial optimization problems. While the authors employ the LOP and the MDP to illustrate cutting-edge optimization technologies, the book is also a tutorial on how to design effective and successful implementations of exact and heuristic procedures alike. This monograph provides the basic principles and fundamental ideas that will enable students and practitioners to create valuable applications based on both exact and heuristic technologies. Specifically, it is aimed at engineers, scientists, operations researchers, and other applications specialists who are looking for the most appropriate and recent optimization tools to solve particular problems. The book provides a broad spectrum of advances in search strategies with a focus on its algorithmic and computational aspects.

Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines - Theory, Algorithms and Applications... Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines - Theory, Algorithms and Applications (Hardcover, 1st ed. 2023)
Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty
R3,893 Discovery Miles 38 930 Ships in 12 - 19 working days

This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions-Chebyshev, Legendre, Gegenbauer, and Jacobi-are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

Operations Research in Space and Air (Hardcover, 2003 ed.): Tito A. Ciriani, G. Fasano, S. Gliozzi, Roberto Tadei Operations Research in Space and Air (Hardcover, 2003 ed.)
Tito A. Ciriani, G. Fasano, S. Gliozzi, Roberto Tadei
R8,554 Discovery Miles 85 540 Ships in 10 - 15 working days

Operations Research in Space and Air is a selection of papers reflecting the experience and expertise of international OR consulting companies and academic groups. The global market and competition play a crucial part in the decision making processes within the Space and Air industries and this book gives practical examples of how advanced applications can be used by Space and Air industry management. The material within the book provides both the basic background for the novice modeler and a useful reference for experienced modelers. Students, researchers and OR practitioners will appreciate the details of the modeling techniques, the processes that have been implemented and the computational results that demonstrate the benefits in applying OR in the Space and Airline industries. Advances in PC and Workstations technology, in optimiza tion engines and in modeling techniques now enable solving problems, never before attained by Operations Research. In recent years the Ital ian OR Society (AfRO, www. airo. org) has organized annual forums for researchers and practitioners to meet together to present and dis cuss the various scientific and technical OR achievements. The OR in Space 8 Air session of AfR02001 and AfR02002 Conferences, together with optimization tools' applications, presented recent results achieved by Alenia Spazio S. p. A. (Turin), Alitalia, Milan Polytechnic and Turin Polytechinc. With additional contributions from academia and indus try they have enabled us to capture, in print, today's 'state-of-the-art' optimization and data mining solutions."

Multi-dimensional Control Problems - Robust Approach (Hardcover, 1st ed. 2022): Anurag Jayswal, Preeti, Savin Treant Multi-dimensional Control Problems - Robust Approach (Hardcover, 1st ed. 2022)
Anurag Jayswal, Preeti, Savin Treant
R3,891 Discovery Miles 38 910 Ships in 12 - 19 working days

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty.

Uncertain Graph and Network Optimization (Hardcover, 1st ed. 2022): Bo Zhang, Jin Peng Uncertain Graph and Network Optimization (Hardcover, 1st ed. 2022)
Bo Zhang, Jin Peng
R3,353 Discovery Miles 33 530 Ships in 10 - 15 working days

This first book focuses on uncertain graph and network optimization. It covers three different main contents: uncertain graph, uncertain programming and uncertain network optimization. It also presents applications of uncertain network optimization in a lot of real problems such as transportation problems, dispatching medical supplies problems and location problems. The book is suitable for researchers, engineers, teachers and students in the field of mathematics, information science, computer science, decision science, management science and engineering, artificial intelligence, industrial engineering, economics and operations research.

Conflict-Controlled Processes (Hardcover, 1997 ed.): A. Chikrii Conflict-Controlled Processes (Hardcover, 1997 ed.)
A. Chikrii
R3,122 Discovery Miles 31 220 Ships in 10 - 15 working days

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. To identify this range of problems we use the term "conflict con trolled processes," coined in recent years. As the name itself does not imply the type of dynamics (difference, ordinary differential, difference-differential, integral, or partial differential equations) the differential games falI within its realms. The problems of search and tracking moving objects are also referred to the field of conflict controlled process. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes. These problems underlie the theory and are of considerable interest to researchers up to now. It should be noted that the methods of "Line of Sight," "Parallel Pursuit," "Proportional N avigation,""Modified Pursuit" and others have been long and well known among engineers engaged in design of rocket and space technology. An abstract theory of dynamic game problems, in its turn, is based on the methods originated by R. Isaacs, L. S. Pontryagin, and N. N. Krasovskii, and on the approaches developed around these methods. At the heart of the book is the Method of Resolving Functions which was realized within the class of quasistrategies for pursuers and then applied to the solution of the problems of "hand-to-hand," group, and succesive pursuit."

Output Feedback Reinforcement Learning Control for Linear Systems (Hardcover, 1st ed. 2023): Syed Ali Asad Rizvi, Zongli Lin Output Feedback Reinforcement Learning Control for Linear Systems (Hardcover, 1st ed. 2023)
Syed Ali Asad Rizvi, Zongli Lin
R4,247 Discovery Miles 42 470 Ships in 12 - 19 working days

This monograph explores the analysis and design of model-free optimal control systems based on reinforcement learning (RL) theory, presenting new methods that overcome recent challenges faced by RL. New developments in the design of sensor data efficient RL algorithms are demonstrated that not only reduce the requirement of sensors by means of output feedback, but also ensure optimality and stability guarantees. A variety of practical challenges are considered, including disturbance rejection, control constraints, and communication delays. Ideas from game theory are incorporated to solve output feedback disturbance rejection problems, and the concepts of low gain feedback control are employed to develop RL controllers that achieve global stability under control constraints. Output Feedback Reinforcement Learning Control for Linear Systems will be a valuable reference for graduate students, control theorists working on optimal control systems, engineers, and applied mathematicians.

Turnpike Phenomenon and Symmetric Optimization  Problems (Hardcover, 1st ed. 2022): Alexander J Zaslavski Turnpike Phenomenon and Symmetric Optimization Problems (Hardcover, 1st ed. 2022)
Alexander J Zaslavski
R3,411 Discovery Miles 34 110 Ships in 10 - 15 working days

Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory. This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, such as mathematicians, mathematical economists, and researchers in crystallography, to name just a few.

Isogeometric Topology Optimization - Methods, Applications and Implementations (Hardcover, 1st ed. 2022): Jie Gao, Liang Gao,... Isogeometric Topology Optimization - Methods, Applications and Implementations (Hardcover, 1st ed. 2022)
Jie Gao, Liang Gao, Mi Xiao
R4,238 Discovery Miles 42 380 Ships in 12 - 19 working days

This book provides a systematic description about the development of Isogeometric Topology Optimization (ITO) method using the density, and then addresses the effectiveness and efficiency of the ITO method on several design problems, including multi-material structures, stress-minimization structures, piezoelectric structures and also with the uniform manufacturability, ultra-lightweight architected materials with extreme bulk/shear moduli, auxetic metamaterials and auxetic meta-composites with the NPRs behavior in microstructures. A detailed MATLAB implementation of the ITO method with an in-house code "IgaTop" is also presented.

Labor and Supply Chain Networks (Hardcover, 1st ed. 2022): Anna Nagurney Labor and Supply Chain Networks (Hardcover, 1st ed. 2022)
Anna Nagurney
R3,894 Discovery Miles 38 940 Ships in 12 - 19 working days

The COVID-19 pandemic has vividly and dramatically demonstrated the importance of supply chains to the functioning of societies and our economies. The discussion in this timely book explores prominent issues concerning supply chain networks and labor. The readership is aimed to include students, researchers, practitioners, and policy-makers, interested in the wide range of topics presented in these pages. Labor has a particular focus as the driver behind supply chains, whether associated with food products, life-saving medicines and supplies, or high tech products that make innovation possible, just to name a few. The impacts of policy interventions, in the form of wage bounds, and their ramifications, in terms of volume of attracted labor, product prices, product volumes, as well as profits, are explored. Profit-maximizing firms are considered (with relevant associated issues such as waste management in the case of the food sector, for example), but also non-profits, as in blood services, as well as humanitarian organizations engaged in disaster relief. The book is filled with many network figures, graphs, and tables with data, both input and output and includes an appendix that provides the foundations of the underlying mathematical methodologies used. The book offers strong evidence for the need to provide a holistic, system-wide perspective for the modeling, analysis, and solution of supply chain problems with the inclusion of the critical labor resources. A formalism using the prism of supply chain networks, which yields a graphic representation of supply chains, consisting of multiple stakeholders, is constructed. Models that capture the behaviors and interactions of single decision-makers as well as multiple decision-makers engaged in supply chain activities of production, transportation, storage, and distribution, are considered. The models capture many realistic constraints faced by firms today, as they seek to produce and deliver products, while dealing with competition, various constraints on labor, a variety of disruptions, labor shortages, challenges associated with proper wage-determination, plus the computation of optimal investments in labor productivity subject to budget constraints. The book provides prescriptive suggestions in terms of how to ameliorate negative impacts of labor disruptions and demonstrate benefits of appropriate wage determination.

Methods of Optimization and Systems Analysis for Problems of Transcomputational Complexity (Hardcover, 2012 ed.): Ivan V.... Methods of Optimization and Systems Analysis for Problems of Transcomputational Complexity (Hardcover, 2012 ed.)
Ivan V. Sergienko
R1,536 Discovery Miles 15 360 Ships in 10 - 15 working days

This work presents lines of investigation and scientific achievements of the Ukrainian school of optimization theory and adjacent disciplines. These include the development of approaches to mathematical theories, methodologies, methods, and application systems for the solution of applied problems in economy, finances, energy saving, agriculture, biology, genetics, environmental protection, hardware and software engineering, information protection, decision making, pattern recognition, self-adapting control of complicated objects, personnel training, etc. The methods developed include sequential analysis of variants, nondifferential optimization, stochastic optimization, discrete optimization, mathematical modeling, econometric modeling, solution of extremum problems on graphs, construction of discrete images and combinatorial recognition, etc. Some of these methods became well known in the world's mathematical community and are now known as classic methods.

Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Hardcover): M. Fukushima, Liqun Qi Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Hardcover)
M. Fukushima, Liqun Qi
R3,136 Discovery Miles 31 360 Ships in 10 - 15 working days

The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997. Responding to our invitation, thirty-eight people agreed to give a talk within the cluster, which enabled us to organize thirteen sessions in total. We think that it was one of the largest and most exciting clusters in the symposium. Thanks to the earnest support by the speakers and the chairpersons, the sessions attracted much attention of the participants and were filled with great enthusiasm of the audience."

Analysis and Synthesis of Nonlinear Control Systems - A Convex Optimisation Approach (Hardcover, 1st ed. 2022): Miguel Bernal,... Analysis and Synthesis of Nonlinear Control Systems - A Convex Optimisation Approach (Hardcover, 1st ed. 2022)
Miguel Bernal, Antonio Sala, Zsofia Lendek, Thierry-Marie Guerra
R4,252 Discovery Miles 42 520 Ships in 12 - 19 working days

This book presents a modern perspective on the modelling, analysis, and synthesis ideas behind convex-optimisation-based control of nonlinear systems: it embeds them in models with convex structures. Analysis and Synthesis of Nonlinear Control Systems begins with an introduction to the topic and a discussion of the problems to be solved. It then explores modelling via convex structures, including quasi-linear parameter-varying, Takagi-Sugeno models, and linear fractional transformation structures. The authors cover stability analysis, addressing Lyapunov functions and the stability of polynomial models, as well as the performance and robustness of the models. With detailed examples, simulations, and programming code, this book will be useful to instructors, researchers, and graduate students interested in nonlinear control systems.

Convex Analysis for Optimization - A Unified Approach (Hardcover, 1st ed. 2020): Jan Brinkhuis Convex Analysis for Optimization - A Unified Approach (Hardcover, 1st ed. 2020)
Jan Brinkhuis
R3,394 Discovery Miles 33 940 Ships in 10 - 15 working days

This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

Evolutionary Multi-Task Optimization - Foundations and Methodologies (Hardcover, 1st ed. 2023): Liang Feng, Abhishek Gupta, Kay... Evolutionary Multi-Task Optimization - Foundations and Methodologies (Hardcover, 1st ed. 2023)
Liang Feng, Abhishek Gupta, Kay Chen Tan, Yew Soon Ong
R4,913 Discovery Miles 49 130 Ships in 12 - 19 working days

A remarkable facet of the human brain is its ability to manage multiple tasks with apparent simultaneity. Knowledge learned from one task can then be used to enhance problem-solving in other related tasks. In machine learning, the idea of leveraging relevant information across related tasks as inductive biases to enhance learning performance has attracted significant interest. In contrast, attempts to emulate the human brain's ability to generalize in optimization - particularly in population-based evolutionary algorithms - have received little attention to date. Recently, a novel evolutionary search paradigm, Evolutionary Multi-Task (EMT) optimization, has been proposed in the realm of evolutionary computation. In contrast to traditional evolutionary searches, which solve a single task in a single run, evolutionary multi-tasking algorithm conducts searches concurrently on multiple search spaces corresponding to different tasks or optimization problems, each possessing a unique function landscape. By exploiting the latent synergies among distinct problems, the superior search performance of EMT optimization in terms of solution quality and convergence speed has been demonstrated in a variety of continuous, discrete, and hybrid (mixture of continuous and discrete) tasks. This book discusses the foundations and methodologies of developing evolutionary multi-tasking algorithms for complex optimization, including in domains characterized by factors such as multiple objectives of interest, high-dimensional search spaces and NP-hardness.

Non-Convex Multi-Objective Optimization (Hardcover, 1st ed. 2017): Panos M. Pardalos, Antanas Zilinskas, Julius Zilinskas Non-Convex Multi-Objective Optimization (Hardcover, 1st ed. 2017)
Panos M. Pardalos, Antanas Zilinskas, Julius Zilinskas
R3,161 Discovery Miles 31 610 Ships in 12 - 19 working days

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

Complementarity: Applications, Algorithms and Extensions (Hardcover, 2001 ed.): Michael C. Ferris, Olvi L. Mangasarian,... Complementarity: Applications, Algorithms and Extensions (Hardcover, 2001 ed.)
Michael C. Ferris, Olvi L. Mangasarian, Jong-Shi Pang
R4,587 Discovery Miles 45 870 Ships in 10 - 15 working days

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar kets, engineering mechanics, optimal control and asset pricing. Further more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed."

Fuzzy Multi-Criteria Decision Making - Theory and Applications with Recent Developments (Hardcover, 2008 ed.): Cengiz Kahraman Fuzzy Multi-Criteria Decision Making - Theory and Applications with Recent Developments (Hardcover, 2008 ed.)
Cengiz Kahraman
R4,469 Discovery Miles 44 690 Ships in 10 - 15 working days

In trying to make a satisfactory decision when imprecise and multicriteria situations are involved, a decision maker has to use a fuzzy multicriteria decision making method. "Fuzzy Multi-Criteria Decision Making" (MCDM) presents fuzzy multiattribute and multiobjective decision-making methodologies by distinguished MCDM researchers.

In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more. Each of the 22 chapters includes practical applications along with new developments/results.

This book may be used as a textbook in graduate operations research, industrial engineering, and economics courses. It will also be an excellent resource, providing new suggestions and directions for further research, for computer programmers, mathematicians, and scientists in a variety of disciplines where multicriteria decision making is needed.

Stochastic Benchmarking - Theory and Applications (Hardcover, 1st ed. 2022): Alireza Amirteimoori, Biresh K. Sahoo, Vincent... Stochastic Benchmarking - Theory and Applications (Hardcover, 1st ed. 2022)
Alireza Amirteimoori, Biresh K. Sahoo, Vincent Charles, Saber Mehdizadeh
R2,865 Discovery Miles 28 650 Ships in 10 - 15 working days

This book introduces readers to benchmarking techniques in the stochastic environment, primarily stochastic data envelopment analysis (DEA), and provides stochastic models in DEA for the possibility of variations in inputs and outputs. It focuses on the application of theories and interpretations of the mathematical programs, which are combined with economic and organizational thinking. The book's main purpose is to shed light on the advantages of the different methods in deterministic and stochastic environments and thoroughly prepare readers to properly use these methods in various cases. Simple examples, along with graphical illustrations and real-world applications in industry, are provided for a better understanding. The models introduced here can be easily used in both theoretical and real-world evaluations. This book is intended for graduate and PhD students, advanced consultants, and practitioners with an interest in quantitative performance evaluation.

Finite Dimensional Convexity and Optimization (Hardcover, 2001 ed.): Monique Florenzano Finite Dimensional Convexity and Optimization (Hardcover, 2001 ed.)
Monique Florenzano; Assisted by P. Gourdel; Cuong Le Van
R2,967 Discovery Miles 29 670 Ships in 10 - 15 working days

The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

Critical Point Theory - Sandwich and Linking Systems (Hardcover, 1st ed. 2020): Martin Schechter Critical Point Theory - Sandwich and Linking Systems (Hardcover, 1st ed. 2020)
Martin Schechter
R3,659 Discovery Miles 36 590 Ships in 10 - 15 working days

This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author's own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book's main subject: applications to problems in mathematics and physics. These include topics such as Schroedinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.

Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing (Hardcover, 2010 Ed.):... Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing (Hardcover, 2010 Ed.)
Michael Elad
R2,702 Discovery Miles 27 020 Ships in 10 - 15 working days

A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham's razor: "Entities should not be multiplied without neces sity. " This principle enabled scientists to select the "best" physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage"spoken"whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the "language" or "dictionary" used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you'll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

Continuous-Time Markov Decision Processes - Borel Space Models and General Control Strategies (Hardcover, 1st ed. 2020): Alexey... Continuous-Time Markov Decision Processes - Borel Space Models and General Control Strategies (Hardcover, 1st ed. 2020)
Alexey Piunovskiy, Yi Zhang; Foreword by Albert Nikolaevich Shiryaev
R2,290 Discovery Miles 22 900 Ships in 12 - 19 working days

This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.

Separable Optimization - Theory and Methods (Hardcover, 2nd ed. 2021): Stefan M. Stefanov Separable Optimization - Theory and Methods (Hardcover, 2nd ed. 2021)
Stefan M. Stefanov
R3,665 Discovery Miles 36 650 Ships in 10 - 15 working days

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.

Optimization of Logistics - Theory and Practice (Hardcover): Turkay Yildiz Optimization of Logistics - Theory and Practice (Hardcover)
Turkay Yildiz
R1,444 R1,233 Discovery Miles 12 330 Save R211 (15%) Ships in 9 - 17 working days

This book comes out from the materials I used to refer while doing my research on the optimization issues in logistics. I brought together some of these materials to form a guidance material on the fundamentals of the optimization concepts along with my own studies on the application of optimization methods. This book consists of two parts and six chapters. The first part of the book, which consists of three chapters, is about introduction to optimization with typical base problems and algorithms for solving problems. The second part of this book consists of three my own researches on the application of optimization methods. Each chapter in this book is independent of each other. I hope you will find this book useful, informative, beneficial and appropriate for your needs.

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