An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming

Qi Zhao () and Zhongwen Chen
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Qi Zhao: School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China
Zhongwen Chen: School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 03, 1-25

Abstract: A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The l1 exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm.

Keywords: Nonlinear semidefinite programming; sequentially semidefinite programming method; global convergence; superlinear convergence (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0217595918500094

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