A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs

In several applications, semideenite programs with nonlinear equality constraints arise. We give two such examples to emphasize the importance of this class of problems. We then propose a new solution method that also applies to smooth nonconvex programs. The method combines ideas of a predictor corrector interior-point method, of the SQP method, and of trust region methods. In particular, we believe that the new method combines the advantages|generality and robustness of trust region methods, local convergence of the SQP-method and data-independence of interior-point methods. Some convergence results are given, and some very preliminary numerical experiments suggest a high robustness of the proposed method.