Finite Dimensional Convexity and Optimization
Springer Science & Business Media, Mar 13, 2001 - Mathematics - 154 pages
This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.
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aff(dom affine hull affine set affinely independent Ai)ie Assume asymptotic cone closed half-spaces compact subset constraints converges convex cone convex function convex hull convex set convex subset Corollary denotes Exercise exists extreme point f is continuous f is convex feasible set fi(x finite function f function from Rn function on Rn G i(dom Hence implies intersection Kuhn-Tucker Conditions Lemma Let f lev<Q level set linear functional linear inequalities linear programming linear programming problem linear subspace Minimize Nc(x necessary and sufficient non-decreasing o/Rn open ball open set optimal solution polyhedral convex set previous proposition Proof prove real numbers relative interior resp ri(C Separation theorem sequence set of Rn Slater Condition subdifferential sublinear function subset of Rn subspace of Rn supporting hyperplane vector verify Vx G Rn Vy G x G Rn