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arXiv · 2302.04567

A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming

Wenhao Fu·Zhongwen Chen
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Abstract

We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a subproblem based on a local model of infeasibility is formulated to determine a corrective step. In the second phase, a search direction that moves toward optimality is computed by minimizing a local model of the objective function. Importantly, regardless of the feasibility of the original problem, the iterative sequence generated by our proposed method converges to a Fritz-John point of a transformed problem, wherein the constraint violation is minimized. Numerical experiments have been conducted on various complex scenarios to demonstrate the effectiveness of our approach.

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Wenhao Fu, Zhongwen Chen. 2023-02-09. A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming. https://doi.org/10.1080/02331934.2024.2345397

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