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Generic Optimality Conditions for Semialgebraic Convex Programs

Abstract : We consider linear optimization over a nonempty convex semialgebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique "active" manifold, around which F is "partly smooth," and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.
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https://hal.inria.fr/hal-00710666
Contributor : Estelle Bouzat <>
Submitted on : Thursday, June 21, 2012 - 2:30:36 PM
Last modification on : Saturday, June 19, 2021 - 3:50:35 AM

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Jérôme Bolte, Aris Daniilidis, Adrian Lewis. Generic Optimality Conditions for Semialgebraic Convex Programs. Mathematics of Operations Research, INFORMS, 2011, 36 (1), pp.55-70. ⟨10.1287/moor.1110.0481⟩. ⟨hal-00710666⟩

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