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Generic identifiability and second-order sufficiency in tame convex optimization

Jerome Bolte(bolte***at***math.jussieu.fr)
Aris Daniilidis(arisd***at***mat.uab.es)
Adrian S. Lewis(aslewis***at***orie.cornell.edu)

Abstract: We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is "partly smooth", ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions hold, guaranteeing smooth behavior of the optimal solution under small perturbations to the objective.

Keywords: tame optimization, partial smoothness, strong maximizer, o-minimal structure.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Research Report, Cornell University, School of ORIE

Download: [PDF]

Entry Submitted: 01/20/2009
Entry Accepted: 01/20/2009
Entry Last Modified: 01/20/2009

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