Generic Optimality Conditions for Semialgebraic Convex Programs

摘要: We consider linear optimization over a nonempty convex semialgebraic feasible region F. Semidefinite programming is an example. If F compact, then for almost every objective there unique optimal solution, lying on “active” manifold, around which “partly smooth,” and the second-order sufficient conditions hold. Perturbing results in smooth variation of solution. The active manifold consists, locally, these perturbed solutions; it independent representation eventually identified by variety iterative algorithms such as proximal projected gradient schemes. These extend to unbounded sets