Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

This book contains selected papers presented at ICGEC 2021, the 14th International Conference on Genetic and Evolutionary Computing, held from October 21-23, 2021 in Jilin City, China. The conference was technically co-sponsored by Springer, Northeast Electric Power University Fujian University of Technology, Shandong University of Science and Technology, and Western Norway University of Applied Sciences. It is intended as an international forum for the researchers and professionals in all areas of genetic and evolutionary computing. And the readers may learn the up-to-date techniques of the mentioned topics, including swarm intelligence, artificial intelligence, information hiding and data mining techniques, which can help them to bring new ideas or apply the designed approaches from the collected papers to their professional jobs.

A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.

Reviews the literature of the Moth-Flame Optimization algorithm; Provides an in-depth analysis of equations, mathematical models, and mechanisms of the Moth-Flame Optimization algorithm; Proposes different variants of the Moth-Flame Optimization algorithm to solve binary, multi-objective, noisy, dynamic, and combinatorial optimization problems; Demonstrates how to design, develop, and test different hybrids of Moth-Flame Optimization algorithm; Introduces several applications areas of the Moth-Flame Optimization algorithm focusing in sustainability.

This book presents new techniques and methods for distributed control and optimization of networked microgrids. Distributed consensus issues under network-based and event-triggered mechanisms are first addressed in a multi-agent system framework, which can explicitly characterize the relationship between communication resources and the control performance. Then, considering the effects of network uncertainties, multi-agent system-based distributed schemes are tailored to solve the fundamental issues of networked microgrids such as distributed frequency regulation, voltage regulation, active power sharing/load sharing, and energy management. The monograph will contribute to stimulating extensive interest of researchers in electrical and control fields.

This book reports on the latest advances in adaptive critic control with robust stabilization for uncertain nonlinear systems. Covering the core theory, novel methods, and a number of typical industrial applications related to the robust adaptive critic control field, it develops a comprehensive framework of robust adaptive strategies, including theoretical analysis, algorithm design, simulation verification, and experimental results. As such, it is of interest to university researchers, graduate students, and engineers in the fields of automation, computer science, and electrical engineering wishing to learn about the fundamental principles, methods, algorithms, and applications in the field of robust adaptive critic control. In addition, it promotes the development of robust adaptive critic control approaches, and the construction of higher-level intelligent systems.

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author's previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

Optimization plays an invaluable role in the exciting and rapidly developing field of computer vision, yet this importance is often overlooked in the literature.

This practical and authoritative text/reference presents a broad introduction to the optimization methods used specifically in computer vision. In order to facilitate understanding, the presentation of the methods is supplemented by simple flow charts, followed by pseudocode implementations that reveal deeper insights into their mode of operation. These discussions are further supported by examples taken from important applications in computer vision.

Topics and features: provides a comprehensive overview of computer vision-related optimization; covers a range of techniques from classical iterative multidimensional optimization to cutting-edge topics of graph cuts and GPU-suited total variation-based optimization; describes in detail the optimization methods employed in computer vision applications; illuminates key concepts with clearly written and step-by-step explanations; presents detailed information on implementation, including pseudocode for most methods.

This easy-to-follow and applications-focused book is an essential resource for researchers and practitioners seeking guidance on implementing specific methods in computer vision.

This book is about optimization techniques and is subdivided into two parts. In the first part a wide overview on optimization theory is presented. Optimization is presented as being composed of five topics, namely: design of experiment, response surface modeling, deterministic optimization, stochastic optimization, and robust engineering design. Each chapter, after presenting the main techniques for each part, draws application oriented conclusions including didactic examples. In the second part some applications are presented to guide the reader through the process of setting up a few optimization exercises, analyzing critically the choices which are made step by step, and showing how the different topics that constitute the optimization theory can be used jointly in an optimization process. The applications which are presented are mainly in the field of thermodynamics and fluid dynamics due to the author's background.

Very little has been published on optimization of pharmaceutical portfolios. Moreover, most of published literature is coming from the commercial side, where probability of technical success (PoS) is treated as fixed, and not as a consequence of development strategy or design. In this book there is a strong focus on impact of study design on PoS and ultimately on the value of portfolio. Design options that are discussed in different chapters are dose-selection strategies, adaptive design and enrichment. Some development strategies that are discussed are indication sequencing, optimal number of programs and optimal decision criteria. This book includes chapters written by authors with very broad backgrounds including financial, clinical, statistical, decision sciences, commercial and regulatory. Many authors have long held executive positions and have been involved with decision making at a product or at a portfolio level. As such, it is expected that this book will attract a very broad audience, including decision makers in pharmaceutical R&D, commercial and financial departments. The intended audience also includes portfolio planners and managers, statisticians, decision scientists and clinicians. Early chapters describe approaches to portfolio optimization from big Pharma and Venture Capital standpoints. They have stronger focus on finances and processes. Later chapters present selected statistical and decision analysis methods for optimizing drug development programs and portfolios. Some methodological chapters are technical; however, with a few exceptions they require a relatively basic knowledge of statistics by a reader.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R. With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going into implementation. Algebraic representation allows for clear understanding and generalization of large applications, and writing formulations is necessary to explain and convey the modeling decisions made. Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B. This book: * Provides and explains code so examples are relatively clear and self-contained. * Emphasizes creating algebraic formulations before implementing. * Focuses on application rather than algorithmic details. * Embodies the philosophy of reproducible research. * Uses open-source tools to ensure access to powerful optimization tools. * Promotes open-source: all materials are available on the author's github repository. * Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R. * Provides code readers can adapt to their own applications . This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.

The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

This book describes the modelling and optimisation of vibration reduction systems in an integrated fashion using nonlinear equations of motion. It proposes an effective optimisation method for determining the basic characteristics of the non-linear visco-elastic elements used in passive vibration reduction systems. In the case of semi-active and active vibration isolators, a design process of the advanced control systems is proposed that makes possible to optimise the controller settings relatively to the selected vibro-isolation criteria. The approach developed here is subsequently tested by means of experimental investigations conducted on various sample vibration reduction systems: passive, semi-active and active. The book presents a biomechanical modelling approach that allows users to select the properties of vibro-isolation systems for different types of oscillation and different optimisation criteria - and can significantly reduce the harmful vibrations that can affect the human body in the process. Further, the book equips readers to evaluate the viscoelastic characteristics of passive systems and design control systems for semi-active and active systems. Modelling and Control Design of Vibration Reduction Systems offers a valuable guide for researchers and practitioners alike. It also provides students and academics with systematic information on the procedures to be followed in the design process for semi-active or active vibration reduction systems.

This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items,  generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to (Schwartz) distribution theory. Elements from the theories of ultra distributions and (Fourier) hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear (bounded and unbounded) operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schroedinger operators, as needed in quantum physics and quantum information theory - are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of (completely) positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire's fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.

In today's world, with an increase in the breadth and scope of real-world engineering optimization problems as well as with the advent of big data, improving the performance and efficiency of algorithms for solving such problems has become an indispensable need for specialists and researchers. In contrast to conventional books in the field that employ traditional single-stage computational, single-dimensional, and single-homogeneous optimization algorithms, this book addresses multiple newfound architectures for meta-heuristic music-inspired optimization algorithms. These proposed algorithms, with multi-stage computational, multi-dimensional, and multi-inhomogeneous structures, bring about a new direction in the architecture of meta-heuristic algorithms for solving complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data. The architectures of these new algorithms may also be appropriate for finding an optimal solution or a Pareto-optimal solution set with higher accuracy and speed in comparison to other optimization algorithms, when feasible regions of the solution space and/or dimensions of the optimization problem increase. This book, unlike conventional books on power systems problems that only consider simple and impractical models, deals with complicated, techno-economic, real-world, large-scale models of power systems operation and planning. Innovative applicable ideas in these models make this book a precious resource for specialists and researchers with a background in power systems operation and planning. Provides an understanding of the optimization problems and algorithms, particularly meta-heuristic optimization algorithms, found in fields such as engineering, economics, management, and operations research; Enhances existing architectures and develops innovative architectures for meta-heuristic music-inspired optimization algorithms in order to deal with complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data; Addresses innovative multi-level, techno-economic, real-world, large-scale, computational-logical frameworks for power systems operation and planning, and illustrates practical training on implementation of the frameworks using the meta-heuristic music-inspired optimization algorithms.

Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative. The volume, which includes new methods as well as review contributions will benefit a wide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.

"Nonconvex Optimal Control and Variational Problems "is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems.

Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with good functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author.

This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community."

This book provides several inventory models for making the right decision in inventory management under different environments. Basically, the optimal ordering policies are determined for situations with and without shortages in production-inventory systems. The chapters in the book include various features of inventory modeling i.e., inflation, deterioration, supply chain, learning, credit financing, carbon emission policy, stock-dependent demand, among others. The book is a useful resource for academicians, researchers, students, practitioners, and managers who can be benefited with the policies provided in the chapters of the book.

This book presents simple design paradigms related to lightweight design, that are derived from an in-depth and theoretically sound analysis based on Pareto theory. It uses numerous examples, including torsion and inflated tubes, to fully explain the theories discussed. Lightweight Construction Principles begins by defining terms in relation to engineering design and optimal design of complex mechanical systems. It then discusses the analytical derivation of the Pareto-optimal set, before applying analytical formulae to optimal design of bent beams. The book moves through numerous case studies of different beam and tube construction including beams subject to bending, thin walled tubes under torsion and truss structures. This book will be of interest to researchers and graduate students in the field of structural optimisation and multi-objective optimization, as well as to practitioners such as design engineers.

This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization - it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields."Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

This book provides different approaches used to analyze, draw attention, and provide an understanding of the advancements in the optimization field across the globe. It brings all of the latest methodologies, tools, and techniques related to optimization and industrial engineering into a single volume to build insights towards the latest advancements in various domains. Applications of Advanced Optimization Techniques in Industrial Engineering includes the basic concept of optimization, techniques, and applications related to industrial engineering. Concepts are introduced in a sequential way along with explanations, illustrations, and solved examples. The book goes on to explore applications of operations research and covers empirical properties of a variety of engineering disciplines. It presents network scheduling, production planning, industrial and manufacturing system issues, and their implications in the real world. The book caters to academicians, researchers, professionals in inventory analytics, business analytics, investment managers, finance firms, storage-related managers, and engineers working in engineering industries and data management fields.

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.