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Operator theory --- 517.98 --- Differential equations, Nonlinear --- -Differential equations, Partial --- -Fredholm operators --- Homotopy groups --- #WWIS:ANAL --- Group theory --- Homotopy theory --- Operators, Fredholm --- Linear operators --- Partial differential equations --- Nonlinear differential equations --- Nonlinear theories --- Functional analysis and operator theory --- Numerical solutions --- Differential equations, Partial --- Fredholm operators. --- Homotopy groups. --- Numerical solutions. --- 517.98 Functional analysis and operator theory --- Fredholm, Opérateurs de --- Équations aux dérivées partielles --- Équations différentielles non linéaires --- Groupes d'homotopie --- Solutions numériques --- Fredholm operators --- Numerical analysis --- Fredholm, Opérateurs de. --- Groupes d'homotopie. --- Solutions numériques.

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This book is based on lectures given in a one-quarter course at UCLA. The aim. is to present som.e of the basic concepts and techniques of Functional Analys.is of relevance to optim.ization problem.s in Control. Com.m.unication and other areas in System. Science. The students are expected to have had an introductory course in Hilbert Space theory. Som.e effort has been m.ade to be self-contained m.ainly in order that the vocabularly used can be clarified. A m.inim.al bibliography is appended. The author is indebted to Jiri Ruzicka and Jerom.e Mersky for help with proof-reading. Profes sor L. Berkovitz looked over and m.ade m.any helpful corn.rn.ents on parts of an early version. Thanks are also due to Trudy Cook for typing the m.anuscript. Grateful acknowledgem.ent is also m.ade of partial support under AFOSR Grant No. 68-1408, Applied Mathem.atics Division, United Stat s Air Force.

Mathematical control systems --- Analytical spaces --- Probability theory --- 681.3*G16 --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Business & Economics --- Economic Theory --- Hilbert space. --- Mathematical optimization. --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Hilbert space --- Mathematical optimization --- Espace de Hilbert --- Optimisation mathématique --- Functional analysis --- Analyse fonctionnelle --- 517.98 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Banach spaces --- Hyperspace --- Inner product spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Functional analysis. --- Programmation (mathématiques)