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A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs

Yuya Yamakawa () and Takayuki Okuno ()
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Yuya Yamakawa: Kyoto University
Takayuki Okuno: Seikei University

Computational Optimization and Applications, 2022, vol. 83, issue 3, No 10, 1027-1064

Abstract: Abstract In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic semidefinite programming (QSDP) subproblems, which we derive from the minimax problem associated with the NSDP. Unlike the existing SQSDP methods, the proposed one allows us to solve those QSDP subproblems inexactly, and each QSDP is feasible. One more remarkable point of the proposed method is that constraint qualifications or boundedness of Lagrange multiplier sequences are not required in the global convergence analysis. Specifically, without assuming such conditions, we prove the global convergence to a point satisfying any of the following: the stationary conditions for the feasibility problem, the approximate-Karush–Kuhn–Tucker (AKKT) conditions, and the trace-AKKT conditions. Finally, we conduct some numerical experiments to examine the efficiency of the proposed method.

Keywords: Nonlinear semidefinite program; Stabilized sequential quadratic semidefinite programming method; Sequential optimality conditions; Global convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00402-x

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