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In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential equations, control theory, and, increasingly, in analysis. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercises. The book begins with an introductory chapter which gives the reader a sampling of what is to come while indicating at an early stage why the subject is of interest. The next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject leading to an efficient, natural, yet powerful body of theory. The last chapter, as its name implies, is a self-contained introduction to the theory of control of ordinary differential equations. End-of-chapter problems also offer scope for deeper understanding. The authors have incorporated in the text a number of new results which clarify the relationships between the different schools of thought in the subject. Their goal is to make nonsmooth analysis accessible to a wider audience. In this spirit, the book is written so as to be used by anyone who has taken a course in functional analysis.

Control theory. --- Nonsmooth optimization. --- Théorie de la commande --- Optimisation non différentiable --- Control theory --- Nonsmooth optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematics. --- System theory. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Mathematical optimization. --- Systems theory. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Philosophy --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Dynamics --- Machine theory

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From its origins in the minimization of integral functionals, the notion of 'variations' has evolved greatly in connection with applications in optimization, equilibrium, and control. It refers not only to constrained movement away from a point, but also to modes of perturbation and approximation that are best describable by 'set convergence', variational convergence of functions and the like. This book develops a unified framework and, in finite dimension, provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, maximal monotone mappings, second-order subderivatives, measurable selections and normal integrands. The changes in this 3rd  printing mainly concern various typographical corrections, and reference omissions that came to light in the previous printings. Many of these reached the authors' notice through their own re-reading, that of their students and a number of colleagues mentioned in the Preface. The authors also included a few telling examples as well as improved a few statements, with slightly weaker assumptions or have strengthened the conclusions in a couple of instances.

Calculus of variations --- Calcul des variations --- 517.97 --- 517.97 Calculus of variations. Mathematical theory of control --- Calculus of variations. Mathematical theory of control --- Calculus of variations. --- Perturbation (mathématiques) --- Perturbation (Mathematics) --- System theory. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Philosophy --- Mathematical analysis --- Analyse fonctionnelle non linéaire --- Analyse fonctionnelle non linéaire --- Perturbation (mathématiques)

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Advances in game theory and economic theory have proceeded hand in hand with that of nonlinear analysis and in particular, convex analysis. These theories motivated mathematicians to provide mathematical tools to deal with optima and equilibria. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its applications to economics and game theory, has written a rigorous and concise-yet still elementary and self-contained- text-book to present mathematical tools needed to solve problems motivated by economics, management sciences, operations research, cooperative and noncooperative games, fuzzy games, etc. It begins with convex and nonsmooth analysis,the foundations of optimization theory and mathematical programming. Nonlinear analysis is next presented in the context of zero-sum games and then, in the framework of set-valued analysis. These results are applied to the main classes of economic equilibria. The text continues with game theory: noncooperative (Nash) equilibria, Pareto optima, core and finally, fuzzy games. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. -(See cont. News remarks).

Nonlinear theories --- Mathematical analysis --- Economics, Mathematical --- Théories non linéaires --- Analyse mathématique --- Mathématiques économiques --- Game theory --- Equilibrium (Economics) --- Théories non linéaires --- Analyse mathématique --- Mathématiques économiques --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Economic theory. --- System theory. --- Calculus of variations. --- Functional Analysis. --- Applications of Mathematics. --- Analysis. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Economic theory --- Political economy --- Social sciences --- Economic man --- 517.1 Mathematical analysis --- Engineering --- Engineering analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Philosophy --- Mathematics

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The ASI on Nonlinear Model Based Process Control (August 10-20, 1997~ Antalya - Turkey) convened as a continuation of a previous ASI which was held in August 1994 in Antalya on Methods of Model Based Process Control in a more general context. In 1994, the contributions and discussions convincingly showed that industrial process control would increasingly rely on nonlinear model based control systems. Therefore, the idea for organizing this ASI was motivated by the success of the first one, the enthusiasm expressed by the scientific community for continuing contact, and the growing incentive for on-line control algorithms for nonlinear processes. This is due to tighter constraints and constantly changing performance objectives that now force the processes to be operated over a wider range of conditions compared to the past, and the fact that many of industrial operations are nonlinear in nature. The ASI intended to review in depth and in a global way the state-of-the-art in nonlinear model based control. The list of lecturers consisted of 12 eminent scientists leading the principal developments in the area, as well as industrial specialists experienced in the application of these techniques. Selected out of a large number of applications, there was a high quality, active audience composed of 59 students from 20 countries. Including family members accompanying the participants, the group formed a large body of92 persons. Out of the 71 participants, 11 were from industry.

Process control --- Nonlinear control theory --- 681.52 --- #TELE:SISTA --- 681.52 Automatic control systems and controllers according to the principle of action --- Automatic control systems and controllers according to the principle of action --- Control of industrial processes --- Industrial process control --- Automatic control --- Manufacturing processes --- Quality control --- Control theory --- Nonlinear theories --- Chemical engineering. --- Electrical engineering. --- Mechanical engineering. --- Calculus of variations. --- Industrial Chemistry/Chemical Engineering. --- Electrical Engineering. --- Mechanical Engineering. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Electric engineering --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Chemistry, Technical --- Metallurgy --- Process control. --- Nonlinear control theory.

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Functional analysis --- Monotonic functions --- Maxima and minima --- Duality theory (Mathematics) --- Monotone operators --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Fonctions monotones --- Functies [Monotoon ] --- Functions [Monotonic ] --- Mathematics duality theory --- Maxima en minima --- Maxima et minima --- Monotone functies --- Monotone operatoren --- Opérateurs monotones --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Opérateurs monotones --- Dualité, Principe de (Mathématiques) --- Functional analysis. --- Operator theory. --- System theory. --- Calculus of variations. --- Functional Analysis. --- Operator Theory. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Systems, Theory of --- Systems science --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Philosophy --- Monotone operators. --- Algebra --- Mathematical analysis --- Topology --- Operator theory