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<p>We develop a reduced sequential quadratic semidefinite programming algorithm for solving nonlinear programming problems with linear matrix inequality (LMI) constraints. The method employs an exact penalty function and a line-search strategy, and it is constructed by combining the classical sequential quadratic programming (SQP) framework with a Schur-complement-based reduction. Global convergence is analyzed under mild conditions. Moreover, under the nondegeneracy condition and the second-order sufficient condition, the sequence generated by the algorithm converges to a strict local minimizer. Moreover, the trial step generated by the quadratic semidefinite programming subproblem exhibits superlinear convergence when the strict complementarity condition is satisfied. Numerical experiments demonstrate the efficiency of the proposed algorithm.</p>

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A reduced SQP-type algorithm for nonlinear semidefinite programming with LMI constraints

  • 期刊论文

  • 发表日期：

    2026年3月11日

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  • Wenhao Fu

摘要

We develop a reduced sequential quadratic semidefinite programming algorithm for solving nonlinear programming problems with linear matrix inequality (LMI) constraints. The method employs an exact penalty function and a line-search strategy, and it is constructed by combining the classical sequential quadratic programming (SQP) framework with a Schur-complement-based reduction. Global convergence is analyzed under mild conditions. Moreover, under the nondegeneracy condition and the second-order sufficient condition, the sequence generated by the algorithm converges to a strict local minimizer. Moreover, the trial step generated by the quadratic semidefinite programming subproblem exhibits superlinear convergence when the strict complementarity condition is satisfied. Numerical experiments demonstrate the efficiency of the proposed algorithm.