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This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems. Contents: Classical Abstract Spaces in Functional Analysis Linear Functionals and Linear Operators Common Function Spaces in Applications Differential Calculus in Normed Vector Spaces Minimization of Functionals Convex Functionals Lower Semicontinuous Functionals.

Functional analysis. --- Convex functions. --- Mathematical optimization. --- Existence theorems. --- Differential equations --- Mathematical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functions, Convex --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- System theory. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory.

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This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems. Contents: Classical Abstract Spaces in Functional Analysis Linear Functionals and Linear Operators Common Function Spaces in Applications Differential Calculus in Normed Vector Spaces Minimization of Functionals Convex Functionals Lower Semicontinuous Functionals

Engineering sciences. Technology --- systeemtheorie --- systeembeheer

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Mathematics --- Engineering sciences. Technology --- Computer. Automation --- toegepaste wiskunde --- automatisering --- systeemtheorie --- systeembeheer