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Smoothing SQP algorithm for semismooth equations with box constraints

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  • Changyu Wang
  • Qian Liu
  • Cheng Ma

Abstract

In this paper, in order to solve semismooth equations with box constraints, we present a class of smoothing SQP algorithms using the regularized-smooth techniques. The main difference of our algorithm from some related literature is that the correspondent objective function arising from the equation system is not required to be continuously differentiable. Under the appropriate conditions, we prove the global convergence theorem, in other words, any accumulation point of the iteration point sequence generated by the proposed algorithm is a KKT point of the corresponding optimization problem with box constraints. Particularly, if an accumulation point of the iteration sequence is a vertex of box constraints and additionally, its corresponding KKT multipliers satisfy strictly complementary conditions, the gradient projection of the iteration sequence finitely terminates at this vertex. Furthermore, under local error bound conditions which are weaker than BD-regular conditions, we show that the proposed algorithm converges superlinearly. Finally, the promising numerical results demonstrate that the proposed smoothing SQP algorithm is an effective method. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Changyu Wang & Qian Liu & Cheng Ma, 2013. "Smoothing SQP algorithm for semismooth equations with box constraints," Computational Optimization and Applications, Springer, vol. 55(2), pages 399-425, June.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:2:p:399-425
    DOI: 10.1007/s10589-012-9524-5
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    References listed on IDEAS

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    1. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
    2. L. Qi & X. J. Tong & D. H. Li, 2004. "Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 601-625, March.
    3. N.H. Xiu & J.Z. Zhang, 2002. "Local Convergence Analysis of Projection-Type Algorithms: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 211-230, October.
    4. Dong-Hui Li & Masao Fukushima, 2001. "Globally Convergent Broyden-Like Methods for Semismooth Equations and Applications to VIP, NCP and MCP," Annals of Operations Research, Springer, vol. 103(1), pages 71-97, March.
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    Cited by:

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    2. Ma, Cheng & Zhang, Liansheng, 2015. "On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 642-656.

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