Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including adaptive observations, sensitivity analysis, parameter estimation and AI applications. The book is useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.

This book presents some sufficient mathematical content with expressive result. The aim of JANO13 is to bring together scientists to discuss their research in all the aspects of mathematics and their applications to different scientific discipline. The main topics of the conference is partial differential equations, mathematical control, numerical analysis and computer science. The conference is interested in recent developments on numerical analysis and real applications in computer science. The latter is viewed as a dynamic branch on the interface of mathematics and informatics that has been growing rapidly over the past several decades. However, its mathematical modelling and interpretation are still not well-explained and need much more clarifications. The main contributions of this book are to give some sufficient mathematical content with expressive results. As a growing field, it is gaining a lot of attention both in media and in the industry world, which will attract the interest of readers from different scientist disciplines.

Unifies the field of optimization with a few geometric principles.

The number of books that can legitimately be called classics in their fields is small indeed, but David Luenberger's Optimization by Vector Space Methods certainly qualifies. Not only does Luenberger clearly demonstrate that a large segment of the field of optimization can be effectively unified by a few geometric principles of linear vector space theory, but his methods have found applications quite removed from the engineering problems to which they were first applied. Nearly 30 years after its initial publication, this book is still among the most frequently cited sources in books and articles on financial optimization.

The book uses functional analysis —the study of linear vector spaces —to impose simple, intuitive interpretations on complex, infinite-dimensional problems. The early chapters offer an introduction to functional analysis, with applications to optimization. Topics addressed include linear space, Hilbert space, least-squares estimation, dual spaces, and linear operators and adjoints. Later chapters deal explicitly with optimization theory, discussing

• Optimization of functionals
• Global theory of constrained optimization
• Local theory of constrained optimization
• Iterative methods of optimization.

End-of-chapter problems constitute a major component of this book and come in two basic varieties. The first consists of miscellaneous mathematical problems and proofs that extend and supplement the theoretical material in the text; the second, optimization problems, illustrates further areas of application and helps the reader formulate and solve practical problems.

For professionals and graduate students in engineering, mathematics, operations research, economics, and business and finance, Optimization by Vector Space Methods is an indispensable source of problem-solving tools.

This book presents the latest trends and developments in multimodal optimization and niching techniques. Most existing optimization methods are designed for locating a single global solution. However, in real-world settings, many problems are "multimodal" by nature, i.e., multiple satisfactory solutions exist. It may be desirable to locate several such solutions before deciding which one to use. Multimodal optimization has been the subject of intense study in the field of population-based meta-heuristic algorithms, e.g., evolutionary algorithms (EAs), for the past few decades. These multimodal optimization techniques are commonly referred to as "niching" methods, because of the nature-inspired "niching" effect that is induced to the solution population targeting at multiple optima. Many niching methods have been developed in the EA community. Some classic examples include crowding, fitness sharing, clearing, derating, restricted tournament selection, speciation, etc. Nevertheless, applying these niching methods to real-world multimodal problems often encounters significant challenges. To facilitate the advance of niching methods in facing these challenges, this edited book highlights the latest developments in niching methods. The included chapters touch on algorithmic improvements and developments, representation, and visualization issues, as well as new research directions, such as preference incorporation in decision making and new application areas. This edited book is a first of this kind specifically on the topic of niching techniques. This book will serve as a valuable reference book both for researchers and practitioners. Although chapters are written in a mutually independent way, Chapter 1 will help novice readers get an overview of the field. It describes the development of the field and its current state and provides a comparative analysis of the IEEE CEC and ACM GECCO niching competitions of recent years, followed by a collection of open research questions and possible research directions that may be tackled in the future.

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and related mathematics.

The book begins with an introduction to software reliability, models and techniques. The book is an informative book covering the strategies needed to assess software failure behaviour and its quality, as well as the application of optimization tools for major managerial decisions related to the software development process. It features a broad range of topics including software reliability assessment and apportionment, optimal allocation and selection decisions and upgradations problems. It moves through a variety of problems related to the evolving field of optimization of software reliability engineering, including software release time, resource allocating, budget planning and warranty models, which are each explored in depth in dedicated chapters. This book provides a comprehensive insight into present-day practices in software reliability engineering, making it relevant to students, researchers, academics and practising consultants and engineers.

The book is devoted to the study of constrained minimization problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such problems are well studied in a finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an objective function and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in optimization. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory. In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under the presence of computational errors. It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors.

This edited book addresses the challenges in managing the operations and supply chain of organizations in the era of internet of things and Industry 4.0. It presents cutting edge research on real world operations related problems, in-depth analyses, and relevant managerial implications. Wide variety of solution approaches such as quantitative, quantitative, and simulations are presented in the context of managing the operations and supply chains. Consisting of selected papers from the XXIII Annual International Conference of Society of Operations Management, this volume is part of a two volume series with the other book consisting of chapters on quantitative decision making. This edited book covers various quantitative models on operations and supply chain management such as inventory optimization, machine learning-operations research integrated model for healthcare systems, game-theoretic analysis of review strategies in truthful information sharing, design of contracts in supply chains, supply chain optimization, inventory routing, and shop floor scheduling. In addition to the quantitative models, several innovative heuristics are proposed for different problems. This book explores qualitative models on improving the performance of small and medium enterprises and petroleum industries and a simulation model for staff allocation in the information technology industry. Finally, this book provides review articles on vaccine supply chains and behavioral operations management. The book throws light on the emerging trends in the use of analytics, optimization, and simulation tools and empirical analysis to improve the performance of operations and supply chains of organizations. It will serve as an essential resource for practitioners, students, faculty members and scholars in operations management and related areas to gain knowledge and pursue high quality research on developments in areas such as managing the resource management and the solution methodology---innovative tools employed in addressing the real world problems and the different optimization techniques.

This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors' approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.

This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

This book is a collection of high-quality research papers presented at the International Conference on Smart and Intelligent Systems (SIS 2021), which will be held in Velagapudi Ramakrishna Siddhartha Engineering College (VRSEC), Andhra Pradesh, India, during February 25-26, 2021, in virtual mode. It highlights how recent informatics intelligent systems have successfully been used to develop innovative smart techniques and infrastructure in the field of modern engineering and technology. The book will also be of interest to those working in the field of computational intelligence, smart computer network and security analysis, control and automation system, cloud computing, fog computing and IoT, smart grid communication, smart cities, solar cell synthesis and their performance, green technology, and many more. The contents of this book prove useful to researchers and professionals.

This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2021), which was hosted online by the University of Bern from August 31 to September 3, 2021, and was jointly organized by the Operations Research Societies of Switzerland (SVOR/ASRO), Germany (GOR e.V.), and Austria (OEGOR). The respective papers discuss classical mathematical optimization, statistics and simulation techniques. These are complemented by computer science methods, and by tools for processing data, designing and implementing information systems. The book also examines recent advances in information technology, which allow massive volumes of data to be processed and enable real-time predictive and prescriptive business analytics to drive decisions and actions. Lastly, it presents a selection of problems that are modeled and treated while taking into account uncertainty, risk management, behavioral issues, etc.

This book provides an essential introduction to Stochastic Programming, especially intended for graduate students. The book begins by exploring a linear programming problem with random parameters, representing a decision problem under uncertainty. Several models for this problem are presented, including the main ones used in Stochastic Programming: recourse models and chance constraint models. The book not only discusses the theoretical properties of these models and algorithms for solving them, but also explains the intrinsic differences between the models. In the book's closing section, several case studies are presented, helping students apply the theory covered to practical problems. The book is based on lecture notes developed for an Econometrics and Operations Research course for master students at the University of Groningen, the Netherlands - the longest-standing Stochastic Programming course worldwide.

This book is one-stop shop which offers essential information one must know and can implement in real-time business expansions to solve engineering problems in various disciplines. It will also help us to make future predictions and decisions using AI algorithms for engineering problems. Machine learning and optimizing techniques provide strong insights into novice users. In the era of big data, there is a need to deal with data science problems in multidisciplinary perspective. In the real world, data comes from various use cases, and there is a need of source specific data science models. Information is drawn from various platforms, channels, and sectors including web-based media, online business locales, medical services studies, and Internet. To understand the trends in the market, data science can take us through various scenarios. It takes help of artificial intelligence and machine learning techniques to design and optimize the algorithms. Big data modelling and visualization techniques of collected data play a vital role in the field of data science. This book targets the researchers from areas of artificial intelligence, machine learning, data science and big data analytics to look for new techniques in business analytics and applications of artificial intelligence in recent businesses.

This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

This book describes the next generation of industry-Industry 4.0-and how it holds the promise of increased flexibility in manufacturing, along with automation, better quality, and improved productivity. The authors discuss how it thus enables companies to cope with the challenges of producing increasingly individualized products with a short lead-time to market and higher quality. The authors posit that intelligent cloud services and resource sharing play an important role in Industry 4.0 anticipated Fourth Industrial Revolution. This book serves the different issues and challenges in cloud resource management CRM techniques with proper propped solution for IT organizations. The book features chapters based on the characteristics of autonomic computing with its applicability in CRM. Each chapter features the techniques and analysis of each mechanism to make better resource management in cloud.

This book examines the economics of natural resource markets and pricing, as well as the field of natural resource economics in general. It presents the key contributions to this field of research, including the pioneering works and contemporary studies. The book highlights the basic principles and ideas underlying theoretical models of resource pricing. The models considered in the book underline the fundamental determinants of resource prices and the economic nature of rents for non-renewable and renewable resources. Besides the classical theory of exhaustible resource economics, the book includes several issues that are of high importance for global economic growth, such as the transition to alternative energy and the economics of climate change. The authors also consider the issues of commodity pricing and a resource cartel's activity that are relevant to the world oil market. The book provides analytical solutions illustrated with numerical examples. It allows an intuitive understanding of the subject and the model inferences through graphical illustrations and an informal introduction. It, therefore, is a must-read for everybody interested in a better understanding of resource prices, resource markets, and resource economics.

This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material. Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano-Sussmann Orbit theorem, Rashevskii-Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.

This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss-Jacobi and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam's stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems - MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

This book dives into radio resource allocation optimizations, a research area for wireless communications, in a pragmatic way and not only includes wireless channel conditions but also incorporates the channel in a simple and practical fashion via well-understood equations. Most importantly, the book presents a practical perspective by modeling channel conditions using terrain-aware propagation which narrows the gap between purely theoretical work and that of industry methods. The provided propagation modeling reflects industry grade scenarios for radio environment map and hence makes the channel based resource allocation presented in the book a field-grade view. Also, the book provides large scale simulations that account for realistic locations with terrain conditions that can produce realistic scenarios applicable in the field. Most portions of the book are accompanied with MATLAB code and occasionally MATLAB/Python/C code. The book is intended for graduate students, academics, researchers of resource allocation in mathematics, computer science, and electrical engineering departments as well as working professionals/engineers in wireless industry.