English

Smooth exact penalty functions II: a reduction to standard exact penalty functions

Optimization and Control 2018-01-30 v2

Abstract

A new class of smooth exact penalty functions was recently introduced by Huyer and Neumaier. In this paper, we prove that the new smooth penalty function for a constrained optimization problem is exact if and only if the standard nonsmooth penalty function for this problem is exact. We also provide some estimates of the exact penalty parameter of the smooth penalty function, and, in particular, show that it asymptotically behaves as the square of the exact penalty parameter of the standard 1\ell_1 penalty function. We briefly discuss a simple way to reduce the exact penalty parameter of the smooth penalty function, and study the effect of nonlinear terms on the exactness of this function.

Keywords

Cite

@article{arxiv.1801.07769,
  title  = {Smooth exact penalty functions II: a reduction to standard exact penalty functions},
  author = {M. V. Dolgopolik},
  journal= {arXiv preprint arXiv:1801.07769},
  year   = {2018}
}

Comments

This is a slightly edited post-peer-review, pre-copyedit version of an article published by Springer in Optimization Letters (2016). The final authenticated version is available online at: http://dx.doi.org/ 10.1007/s11590-015-0961-9