A new class of exact penalty functions and penalty algorithms

Authors:
Changyu Wang;Cheng Ma;Jinchuan Zhou
Affiliations:
Institute of Operations Research, Qufu Normal University, Qufu, China;College of Business, Qingdao University, Qingdao, China;Department of Mathematics, School of Science, Shandong University of Technology, Zibo, China
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

For nonlinear programming problems, we propose a new class of smooth exact penalty functions, which includes both barrier-type and exterior-type penalty functions as special cases. We develop necessary and sufficient conditions for exact penalty property and inverse proposition of exact penalization, respectively. Furthermore, we establish the equivalent relationship between these penalty functions and classical simple exact penalty functions in the sense of exactness property. In addition, a feasible penalty function algorithm is proposed. The convergence analysis of the algorithm is presented, including the global convergence property and finite termination property. Finally, numerical results are reported.