A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs

Abstract

. In several applications, semidefinite 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. AMS 1991 subject classification. Primary: 90C. Key words. Predictor corrector method, SQP method, trust region method, semidefinite program. 1. Introduction This work was motivated by two applications from semidefinite programming with nonlinear equality constraints as outlin..