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A new class of exact penalty functions and penalty algorithms

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  • Changyu Wang
  • Cheng Ma
  • Jinchuan Zhou

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Changyu Wang & Cheng Ma & Jinchuan Zhou, 2014. "A new class of exact penalty functions and penalty algorithms," Journal of Global Optimization, Springer, vol. 58(1), pages 51-73, January.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:1:p:51-73
    DOI: 10.1007/s10898-013-0111-9
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    References listed on IDEAS

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    1. Antczak, Tadeusz, 2009. "Exact penalty functions method for mathematical programming problems involving invex functions," European Journal of Operational Research, Elsevier, vol. 198(1), pages 29-36, October.
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    Cited by:

    1. Lei Zhang & Yang Liu & Jianneng Chen & Heng Zhou & Yunsheng Jiang & Junhua Tong & Lianlian Wu, 2023. "Trajectory Synthesis and Optimization Design of an Unmanned Five-Bar Vegetable Factory Packing Machine Based on NSGA-II and Grey Relation Analysis," Agriculture, MDPI, vol. 13(7), pages 1-21, July.
    2. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 728-744, March.
    3. Jiachen Ju & Qian Liu, 2020. "Convergence properties of a class of exact penalty methods for semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 383-403, June.
    4. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 745-762, March.
    5. Qian Liu & Yuqing Xu & Yang Zhou, 2020. "A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 745-768, April.

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