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In this paper, we present a stabilized sequential quadratic semidefiniteprogramming (SQSDP) method for nonlinear semidefinite programming (NSDP)problems and prove its local convergence. The stabilized SQSDP method isoriginally developed to solve degenerate NSDP problems and is based on thestabilized sequential programming (SQP) methods for nonlinear programming (NLP)problems. Although some SQP-type methods for NSDP problems have been proposed,most of them are SQSDP methods which are based on the SQP methods for NLPproblems, and there are few researches regarding the stabilized SQSDP methods.In particular, there is room for the development of locally fast convergentstabilized SQSDP methods. We prove not only superlinear but also quadraticconvergence of the proposed method under some assumptions without the strictcomplementarity condition, constraint nondegeneracy, and strong second-ordersufficient condition. Finally, we conduct some numerical experiments to confirmthe performance of the proposed method.

Superlinear and quadratic convergence of a stabilized sequential  quadratic semidefinite programming method for nonlinear semidefinite  programming problems