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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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This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.

Mathematical optimization. --- Control theory. --- Nonsmooth optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Dynamics --- Machine theory --- Optimization.

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This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.   Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory.

Funcational analysis. --- Mathematics. --- Nonsmooth optimization. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Nonsmooth analysis --- Optimization, Nonsmooth --- Functional analysis. --- Optimization. --- Continuous Optimization. --- Functional Analysis. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical optimization --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics. Audience This book is intended for researchers in mathematics and mechanics.

Engineering. --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Mechanical engineering. --- Mechanical Engineering. --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- 517.1 Mathematical analysis --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Mathematics --- Mechanics, Analytic. --- Nonsmooth optimization. --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Analytical mechanics --- Kinetics --- Global analysis (Mathematics). --- Computer science --- Mathematics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Moreau, Jean Jacques, --- Moreau, J. J.