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The Nonlinear Programming Problem
Linear Inequalities and Theorems
4 Theorems of the alternative
11 other sections not shown
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Arrow-Hurwicz-Uzawa constraint qualification Chap concave functions contradicts convex combination convex function convex set Corollary denote dual problem duality theorem equality constraints equivalent exists Farkas feasible point fg(x FJSP follows Fritz John func function A numerical function on Rn g be differentiable G Rn g satisfies gi(x Gordan's theorem Hence Hessian matrix inequality infimum Lemma let g linear programming linearly independent lower semicontinuous m-dimensional vector function Mangasarian matrix maximum minimization problem minimum necessary optimality conditions necessary optimality criteria nonempty nonlinear programming numerical function defined open ball open convex set open set pf(x programming problem PROOF Let pseudoconcave pseudoconvex qh(x quasiconvex function real number rows saddlepoint problem semidefinite set in Rn set T C Rn solution of MP solves MP strictly concave strictly convex strictly quasiconcave strictly quasiconvex subsets of Rn Theorem Let tion ug(x vectors in Rn zero