The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.

2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.

This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.

This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.

This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has five parts. The first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The fourth part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future: task and tool design and new forms of activity via connectivity and computer games.

Intelligent Decision Technologies (IDT) seeks an interchange of research on intelligent systems and intelligent technologies which enhance or improve decision making in industry, government and academia. The focus is interdisciplinary in nature, and includes research on all aspects of intelligent decision technologies, from fundamental development to the applied system. This volume represents leading research from the Third KES International Symposium on Intelligent Decision Technologies (KES IDT’11), hosted and organized by the University of Piraeus, Greece, in conjunction with KES International. The symposium was concerned with theory, design, development, implementation, testing and evaluation of intelligent decision systems. Topics include decision making theory, intelligent agents, fuzzy logic, multi-agent systems, Bayesian networks, optimization, artificial neural networks, genetic algorithms, expert systems, decision support systems, geographic information systems, case-based reasoning, time series, knowledge management systems, rough sets, spatial decision analysis, and multi-criteria decision analysis. These technologies have the potential to revolutionize decision making in many areas of management, healthcare, international business, finance, accounting, marketing, military applications, ecommerce, network management, crisis response, building design, information retrieval, and disaster recovery for a better future. The symposium was concerned with theory, design, development, implementation, testing and evaluation of intelligent decision systems. Topics include decision making theory, intelligent agents, fuzzy logic, multi-agent systems, Bayesian networks, optimization, artificial neural networks, genetic algorithms, expert systems, decision support systems, geographic information systems, case-based reasoning, time series, knowledge management systems, rough sets, spatial decision analysis, and multi-criteria decision analysis. These technologies have the potential to revolutionize decision making in many areas of management, healthcare, international business, finance, accounting, marketing, military applications, ecommerce, network management, crisis response, building design, information retrieval, and disaster recovery for a better future.

This book opens up new ways to develop mathematical models and optimization methods for interdependent energy infrastructures, ranging from the electricity network, natural gas network, district heating network, and electrified transportation network. The authors provide methods to help analyze, design, and operate the integrated energy system more efficiently and reliably, and constitute a foundational basis for decision support tools for the next-generation energy network. Chapters present new operation models of the coupled energy infrastructure and the application of new methodologies including convex optimization, robust optimization, and equilibrium constrained optimization. Four appendices provide students and researchers with helpful tutorials on advanced optimization methods: Basics of Linear and Conic Programs; Formulation Tricks in Integer Programming; Basics of Robust Optimization; Equilibrium Problems. This book provides theoretical foundation and technical applications for energy system integration, and the the interdisciplinary research presented will be useful to readers in many fields including electrical engineering, civil engineering, and industrial engineering.

This book provides an in-depth analysis of investment problems pertaining to electric energy infrastructure, including both generation and transmission facilities. The analysis encompasses decision-making tools for expansion planning, reinforcement, and the selection and timing of investment options. In this regard, the book provides an up-to-date description of analytical tools to address challenging investment questions such as: How can we expand and/or reinforce our aging electricity transmission infrastructure? How can we expand the transmission network of a given region to integrate significant amounts of renewable generation? How can we expand generation facilities to achieve a low-carbon electricity production system? How can we expand the generation system while ensuring appropriate levels of flexibility to accommodate both demand-related and production-related uncertainties? How can we choose among alternative production facilities? What is the right time to invest in a given production or transmission facility? Written in a tutorial style and modular format, the book includes a wealth of illustrative examples to facilitate comprehension. It is intended for advanced undergraduate and graduate students in the fields of electric energy systems, operations research, management science, and economics. Practitioners in the electric energy sector will also benefit from the concepts and techniques presented here.

A unified treatment of the latest game theoretic approaches for designing, modeling, and optimizing emerging wireless communication networks. Covering theory, analytical tools, and applications, it is ideal for researchers and graduate students in academia and industry designing efficient, scalable and robust protocols for future wireless networks.