A perturbation view of level-set methods for convex optimization

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Abstract

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies ε-infeasible points that do not converge to a feasible point as ε tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater’s constraint qualification.

BiBTeX

@ARTICLE{EstrinFriedlander2020perturbation,
  author = {Ron Estrin and Michael P. Friedlander},
  title = {A perturbation view of level-set methods for convex optimization},
  year = {2020},
  journal = {Optimization Letters},
  doi = {10.1007/s11590-020-01609-9}
}