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.
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Acknowledgments
The authors would like to thank referees for their constructive comments and suggestions, which significantly improved the presentation of the paper. The authors also thank Prof. Zhiyuan Tian in Qingdao University for his help.
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This research was supported by the National Natural Science Foundation of China (10971118, 11271226, 11271233, 11101248, 10901096).
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Wang, C., Ma, C. & Zhou, J. A new class of exact penalty functions and penalty algorithms. J Glob Optim 58, 51–73 (2014). https://doi.org/10.1007/s10898-013-0111-9
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DOI: https://doi.org/10.1007/s10898-013-0111-9
Keywords
- Nonlinear programming
- Smooth and exact penalty function
- Constraint qualifications
- Penalty function algorithms