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A system of nonsmooth equations solver based upon subgradient method

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  • Long, Qiang
  • Wu, Changzhi
  • Wang, Xiangyu

Abstract

In this paper, a subgradient method is developed to solve the system of (nonsmooth) equations. First, the system of (nonsmooth) equations is transformed into a nonsmooth optimization problem with zero minimal objective function value. Then, a subgradient method is applied to solve the nonsmooth optimization problem. During the processes, the pre-known optimal objective function value is adopted to update step sizes. The corresponding convergence results are established as well. Several numerical experiments and applications show that the proposed method is efficient and robust.

Suggested Citation

  • Long, Qiang & Wu, Changzhi & Wang, Xiangyu, 2015. "A system of nonsmooth equations solver based upon subgradient method," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 284-299.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:284-299
    DOI: 10.1016/j.amc.2014.11.064
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    References listed on IDEAS

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    1. H. Xu & B. M. Glover, 1997. "New Version of the Newton Method for Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 395-415, May.
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    3. H. Xu & X. W. Chang, 1997. "Approximate Newton Methods for Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 373-394, May.
    4. Z. Y. Wu & L. S. Zhang & K. L. Teo & F. S. Bai, 2005. "New Modified Function Method for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 181-203, April.
    5. Jong-Shi Pang, 1990. "Newton's Method for B-Differentiable Equations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 311-341, May.
    6. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    7. D. H. Li & N. Yamashita & M. Fukushima, 2001. "Nonsmooth Equation Based BFGS Method for Solving KKT Systems in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 123-167, April.
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