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A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming

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Abstract

We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming. At each iteration, we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not. The search direction is generated by a piecewise quadratic-linear model of the exact penalty function. The penalty parameter is only related to the information of the current iterate point. The line search strategy is a penalty-free one. Global and local convergence are analyzed under suitable conditions. We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.

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Authors and Affiliations

  1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, 215009, China

    Wen-hao Fu

  2. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Zhong-wen Chen

Authors
  1. Wen-hao Fu
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  2. Zhong-wen Chen
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Corresponding authors

Correspondence to Wen-hao Fu or Zhong-wen Chen.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11871362).

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Fu, Wh., Chen, Zw. A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming. Acta Math. Appl. Sin. Engl. Ser. 38, 388–409 (2022). https://doi.org/10.1007/s10255-022-1081-9

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  • DOI: https://doi.org/10.1007/s10255-022-1081-9

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