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arXiv · 0901.3117

Generic identifiability and second-order sufficiency in tame convex optimization

J. Bolte·A. Daniilidis·A. S. Lewis
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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.

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J. Bolte, A. Daniilidis, A. S. Lewis. 2009-01-20. Generic identifiability and second-order sufficiency in tame convex optimization. https://arxiv.org/abs/0901.3117

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