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 ${\ell }_1$ 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.

arXiv commentThis 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

References in corpus (1)

• Smooth Exact Penalty Functions: A General Approach

Cited by in corpus (4)

• Exact Penalty Functions for Optimal Control Problems I: Main Theorem and Free-Endpoint Problems
• A unifying theory of exactness of linear penalty functions II: parametric penalty functions
• A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness
• A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness