Abstract
In this paper, we present a line search exact penalty method for solving nonlinear semidefinite programming (SDP) problem. Compared with the traditional sequential semidefinite programming (SSDP) method which requires that the subproblem at every iterate point is compatible, this method is more practical. We first use a robust subproblem, which is always feasible, to get a detective step, then compute a search direction either from a traditional SSDP subproblem or a quadratic optimization subproblem with the penalty term. This two-phase strategy with the $$l_1$$ exact penalty function is employed to promote the global convergence, which is analyzed without assuming any constraint qualifications. Some preliminary numerical results are reported.
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