In this chapter we concentrate on properties of convex sets in a Hilbert space and some of the related problems of importance in application to convex programming: variational problems for convex functions over convex sets, central to which are the Kuhn-Tucker theorem and the minimax theorem of von Neumann, which in turn are based on the “separation” theorems for convex sets. A related result is the Farkas lemma in finite dimensions which finds application in network flow problems.
KeywordsHilbert Space Boundary Point Interior Point Convex Program Positive Cone
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