A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs

Florian Jarre

In several applications, semidefinite programs with nonlinear equality constraints arise. Two such examples are presented to emphasize the importance of this class of problems. To solve such problems we propose an interior-point method in which the usual linear systems of the Newton step and of the predictor step are replaced by quadratically constrained quadratic programs. These QQP's are of a special structure and can be solved directly. In addition, the QQP's allow for a special line search which effects that the algorithm is applicable to nonconvex programs. Some convergence results are given, and some very preliminary numerical experiments suggest a high robustness of the proposed method. We believe that the new method combines the advantages---generality and robustness of trust region methods, and data-independence and fast local convergence of interior-point methods. The method, and in particular, the applications offer a lot of further reseach possibilities.

Report, Universitaet Trier, August 1998.

Contact: jarre@mathematik.uni-wuerzburg.de