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Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions

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  • Tang, Chun-ming
  • Jian, Jin-bao

Abstract

In this paper, we propose a strongly sub-feasible direction method for the solution of inequality constrained optimization problems whose objective functions are not necessarily differentiable. The algorithm combines the subgradient aggregation technique with the ideas of generalized cutting plane method and of strongly sub-feasible direction method, and as results a new search direction finding subproblem and a new line search strategy are presented. The algorithm can not only accept infeasible starting points but also preserve the “strong sub-feasibility” of the current iteration without unduly increasing the objective value. Moreover, once a feasible iterate occurs, it becomes automatically a feasible descent algorithm. Global convergence is proved, and some preliminary numerical results show that the proposed algorithm is efficient.

Suggested Citation

  • Tang, Chun-ming & Jian, Jin-bao, 2012. "Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions," European Journal of Operational Research, Elsevier, vol. 218(1), pages 28-37.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:1:p:28-37
    DOI: 10.1016/j.ejor.2011.10.055
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    References listed on IDEAS

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    1. J. B. Jian, 2006. "New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 109-130, April.
    2. Jian, Jin-Bao & Tang, Chun-Ming & Zheng, Hai-Yan, 2010. "Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 645-657, February.
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    Cited by:

    1. Xiaoliang Wang & Liping Pang & Qi Wu & Mingkun Zhang, 2021. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    2. Tang, Chunming & Liu, Shuai & Jian, Jinbao & Ou, Xiaomei, 2020. "A multi-step doubly stabilized bundle method for nonsmooth convex optimization," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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