Penalty functions with a small penalty parameter

A. M. Rubinov, Xiaoqi Yang, A. M. Bagirov

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)


In this article, we study the nonlinear penalization of a constrained optimization problem and show that the least exact penalty parameter of an equivalent parametric optimization problem can be diminished. We apply the theory of increasing positively homogeneous (IPH) functions so as to derive a simple formula for computing the least exact penalty parameter for the classical penalty function through perturbation function. We establish that various equivalent parametric reformulations of constrained optimization problems lead to reduction of exact penalty parameters. To construct a Lipschitz penalty function with a small exact penalty parameter for a Lipschitz programming problem, we make a transformation to the objective function by virtue of an increasing concave function. We present results of numerical experiments, which demonstrate that the Lipschitz penalty function with a small penalty parameter is more suitable for solving some nonconvex constrained problems than the classical penalty function.
Original languageEnglish
Pages (from-to)931-964
Number of pages34
JournalOptimization Methods and Software
Issue number5
Publication statusPublished - 1 Oct 2002


  • IPH functions
  • Least exact penalty parameter
  • Penalty functions

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics


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