Abstract
In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear semideflnite programming. At each iteration, two systems of linear equations with the same coefficient matrix are solved to determine search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for traditional filter methods. The proposed algorithm is globally convergent under some mild conditions. Preliminary numerical results indicate that the proposed algorithm is comparable.
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The authors would like to thank the two anonymous referees for their valuable suggestions which have improved the final presentation of the paper.
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The research is supported by the National Natural Science Foundation (No.11561005), the National Science Foundation of Guangxi (No.2016GXNSFAA380248).
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Li, Jl., Yang, Zp., Wu, Jq. et al. A New QP-free Algorithm Without a Penalty Function or a Filter for Nonlinear Semidefinite Programming. Acta Math. Appl. Sin. Engl. Ser. 36, 714–736 (2020). https://doi.org/10.1007/s10255-020-0964-x
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DOI: https://doi.org/10.1007/s10255-020-0964-x