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Convexity spaces.

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All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-c

Holomorphic functions. --- Functional analysis. --- Convexity spaces. --- Convex surfaces. --- Complexes. --- Linear complexes --- Algebras, Linear --- Coordinates --- Geometry --- Line geometry --- Transformations (Mathematics) --- Convex areas --- Convex domains --- Surfaces --- Spaces, Convexity --- Convex sets --- Vector spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions, Holomorphic --- Functions of several complex variables

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The present book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfe-type Duality, Mond-Weir type Duality, Mixed type Duality for Multiobjective optimization problems such as Nonlinear programming problems, Fractional programming problems, Nonsmooth programming problems, Nondifferentiable programming problems, Variational and Control problems under various types of generalized convexity assumptions.

Convex functions. --- Convexity spaces. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Functions, Convex --- Mathematics. --- Operations research. --- Decision making. --- Potential theory (Mathematics). --- Mathematical models. --- Calculus of variations. --- Potential Theory. --- Mathematical Modeling and Industrial Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Models, Mathematical --- Simulation methods --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Decision making --- Operations research --- System analysis --- Functions of real variables --- Operations Research/Decision Theory.