Generic Optimality Conditions for Semialgebraic Convex Programs

Jérôme Bolte 1 Aris Daniilidis 2 Adrian Lewis 3
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
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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Mathematics of Operations Research, INFORMS, 2011, 36 (1), pp.55-70. 〈10.1287/moor.1110.0481〉
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Soumis le : jeudi 21 juin 2012 - 14:30:36
Dernière modification le : vendredi 31 août 2018 - 08:47:05

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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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