Generic identifiability and second-order sufficiency in tame convex optimization
Optimization and Control
2009-01-21 v1 Numerical Analysis
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.
Cite
@article{arxiv.0901.3117,
title = {Generic identifiability and second-order sufficiency in tame convex optimization},
author = {J. Bolte and A. Daniilidis and A. S. Lewis},
journal= {arXiv preprint arXiv:0901.3117},
year = {2009}
}