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nonsmooth analysis --- nonsmooth optimization --- variational analysis --- equilibrium problems --- stochastic optimization --- bilevel optimization --- Nonsmooth optimization --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Nonsmooth optimization.

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The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.

Control theory --- Nonsmooth optimization --- Systems engineering --- Engineering systems --- System engineering --- Engineering --- Industrial engineering --- System analysis --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Dynamics --- Machine theory --- Research. --- Design and construction

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The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and finally presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed; this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.

Nonsmooth optimization. --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Global analysis (Mathematics). --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained. This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers.

Variational inequalities (Mathematics) --- Nonsmooth optimization. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Inequalities, Variational (Mathematics) --- Differential inequalities --- Differential equations, partial. --- Mathematics. --- Functional Analysis. --- Partial Differential Equations. --- Applications of Mathematics. --- Math --- Science --- Partial differential equations --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations

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This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters briefly discuss two concrete models (a linear fractional vector optimization and a traffic equilibrium problem) whose analysis can benefit greatly from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of continuity and differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequalities where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequalities under linear perturbations are studied in three other chapters. One special feature of this book is that when a certain property of a characteristic map or function is investigated, the authors always try first to establish necessary conditions for it to hold, then they go on to study whether the obtained necessary conditions are sufficient ones. This helps to clarify the structures of the two classes of problems under consideration. The qualitative results can be used for dealing with algorithms and applications related to quadratic programming problems and affine variational inequalities. Audience This book is intended for graduate and postgraduate students in applied mathematics, as well as researchers in the fields of nonlinear programming and equilibrium problems. It can be used for some advanced courses on nonconvex quadratic programming and affine variational inequalities.

Quadratic programming. --- Nonsmooth optimization. --- Variational inequalities (Mathematics) --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Nonlinear programming --- Mathematical optimization. --- Operations research. --- Optimization. --- Operations Research, Management Science. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Management science. --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Quantitative business analysis --- Statistical decision --- Decision making