  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.

Optimization and Control