This lecture covers the Karush-Kuhn-Tucker (KKT) conditions in convex optimization, including dual cones, properties of the dual cone, problems with generalized inequalities, SDP duality, complementary slackness, and the relevance of the KKT conditions. It also explores separable problems, closed functions, strict separating hyperplane theorem, representation of convex closed sets, convex hulls, and convex hull of a function.
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