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

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