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This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations. Careful distinction is made throughout the analysis between "local" and "global" maximum principles.Originally published in 1977.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical optimization. --- Calcul des variations --- Optimisation

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There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference[248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe’s work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe’s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented.

Malliavin calculus. --- Stochastic analysis. --- Calculus, Malliavin --- Stochastic analysis --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Distribution (Probability theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Calculus of variations. --- Malliavin, Calcul de. --- Calcul des variations.

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Convex analysis and variational problems

Functional analysis --- Mathematical optimization --- Convex functions --- Calculus of variations --- Mathematical optimization. --- Convex functions. --- Calculus of variations. --- 517 --- 517 Analysis --- Analysis --- Optimisation mathématique --- Fonctions convexes --- Calcul des variations --- ELSEVIER-B EPUB-LIV-FT --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functions, Convex --- Functions of real variables --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis

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The computation and theory of optimal control

Control theory. --- Control theory. Mathematical optimization. --- Mathematical optimization. --- Control theory --- Mathematical optimization --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory --- Calcul des variations --- Theorie du controle --- Methodes numeriques --- Optimisation --- Controle optimal

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System analysis --- Calculus of variations --- Mathematical analysis --- Analyse de systèmes. --- Calcul des variations. --- Analyse mathématique. --- Calculus of variations. --- Mathematical analysis. --- System analysis. --- Network theory --- Systems analysis --- Advanced calculus --- Analysis (Mathematics) --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis --- System theory --- Mathematical optimization --- Algebra --- Maxima and minima --- Network analysis --- Network science --- Systems Analysis --- Analyse de systèmes --- Calcul des variations --- Analyse mathématique --- systems analysis. --- Agent-Based Modeling --- Analysis, Systems --- Complexity Analysis --- System Dynamics Analysis --- Systems Approach --- Systems Medicine --- Systems Oriented Approach --- Systems Thinking --- Agent Based Modeling --- Agent-Based Modelings --- Analyses, Complexity --- Analyses, System Dynamics --- Analyses, Systems --- Analysis, Complexity --- Analysis, System Dynamics --- Approach, Systems --- Approach, Systems Oriented --- Approachs, Systems --- Approachs, Systems Oriented --- Complexity Analyses --- Dynamics Analyses, System --- Dynamics Analysis, System --- Medicine, Systems --- Medicines, Systems --- Modeling, Agent-Based --- Modelings, Agent-Based --- System Dynamics Analyses --- Systems Analyses --- Systems Approachs --- Systems Medicines --- Systems Oriented Approachs --- Systems Thinkings --- Thinking, Systems --- Thinkings, Systems --- Research --- Systems Theory