Optimization and Nonsmooth Analysis
Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.
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apply assertion Banach space belongs to 6f(x bounded calculus of variations Chapter Clarke classical closed compact completes the proof cone constant constraints converging convex analysis convex cone convex function convex hull convex set Corollary deduce defined definition denote differential inclusion directionally Lipschitz element epi f equivalent example exists f is Lipschitz f is regular finite fº(x follows function f given gradient Hamilton–Jacobi equation hypertangent hypotheses implies inequality Lemma Let f lim sup Lipschitz condition Lipschitz function locally Lipschitz lower semicontinuous mapping Math matrix maximum principle measurable function measurable selection minimizing multifunction necessary conditions neighborhood nondifferentiable nonempty nonnegative nonsmooth normal Note optimal control problem problem of Bolza Proposition Let result Rockafellar satisfies Section sequence ſº solution solves strictly differentiable subset suffices to prove support function suppose Theorem Let trajectory upper semicontinuous vector