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INTR0DUCTI0N EXAMPLES SURVEY
NECESSARY 0PTIMALITY C0NDITI0NS
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0bviously affine manifold application approximation problem arbitrary assume Banach space calculus of variations Cauchy sequence cl(A closed hyperplane compact constraint qualification contradiction converges convex cone convex functions convex program convex sets define Definition differentiable dual program epi f equations Example f A,B FARKAS-Lemma finite dimensional follows geometric halfspace hence hyperplane H(l,y inradius ip(y Lagrange multiplier Lemma linear program linear subspace Maximize Minimize f(x necessary optimality conditions nonnegative halfspace normal form normed linear space optimal control optimization problem production plan program dual proof prove quadratic program Remark resp separation theorem sequence side condition solution solvable strong duality theorem subset supporting hyperplane Suppose given theory tion triangle vector weak duality theorem weakly sequentially x(tQ