- Title
- Penalty functions with a small penalty parameter
- Creator
- Rubinov, Alex; Yang, Xiao; Bagirov, Adil
- Date
- 2002
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/31692
- Identifier
- vital:768
- Identifier
-
https://doi.org/10.1080/1055678021000066058
- Identifier
- ISSN:1055-6788
- Abstract
- 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.
- Publisher
- Taylor & Francis Ltd.
- Relation
- Optimization Methods and Software Vol. 17, no. 5 (2002), p. 931-964
- Rights
- Copyright Taylor & Francis
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0802 Computation Theory and Mathematics; IPH functions; Least exact penalty parameter; Penalty functions; Mathematical transformations; Numerical methods; Optimisation; Perturbation techniques; Problem solving
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