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A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization

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Abstract

The gradient sampling (GS) algorithm for minimizing a nonconvex, nonsmooth function was proposed by Burke et al. (SIAM J Optim 15:751–779, 2005), whose most interesting feature is the use of randomly sampled gradients instead of subgradients. In this paper, combining the GS technique with the sequential quadratic programming (SQP) method, we present a feasible SQP-GS algorithm that extends the GS algorithm to nonconvex, nonsmooth constrained optimization. The proposed algorithm generates a sequence of feasible iterates, and guarantees that the objective function is monotonically decreasing. Global convergence is proved in the sense that, with probability one, every cluster point of the iterative sequence is stationary for the improvement function. Finally, some preliminary numerical results show that the proposed algorithm is effective.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, People’s Republic of China

    Chun-ming Tang, Shuai Liu & Jian-ling Li

  2. College of Mathematics and Information Science, Yulin Normal University, Yulin, 537000, People’s Republic of China

    Jin-bao Jian

  3. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, People’s Republic of China

    Jin-bao Jian

Authors
  1. Chun-ming Tang
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  2. Shuai Liu
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  3. Jin-bao Jian
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  4. Jian-ling Li
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Correspondence to Jin-bao Jian.

Additional information

Project supported by the National Natural Science Foundation (No. 11271086), Tianyuan Fund for Mathematics (No. 11126341), Innovation Group of Talents Highland of Guangxi Higher School, and Science Foundation of Guangxi Education Department (No. 201102ZD002) of China.

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Tang, Cm., Liu, S., Jian, Jb. et al. A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization. Numer Algor 65, 1–22 (2014). https://doi.org/10.1007/s11075-012-9692-5

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  • DOI: https://doi.org/10.1007/s11075-012-9692-5

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