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