Article ID: | iaor20042320 |
Country: | Netherlands |
Volume: | 1 |
Issue: | 4 |
Start Page Number: | 347 |
End Page Number: | 372 |
Publication Date: | Dec 2000 |
Journal: | Optimization and Engineering |
Authors: | Jarre Florian |
In several applications, semidefinite programs arise in which the matrix depends nonlinearly on the unknown variables. We propose a new solution method for such semidefinite programs that also applies to other smooth nonconvex programs. The method is an extension of a primal predictor corrector interior method to nonconvex programs. The predictor steps are based on Dikin ellipsoids of a ‘convexified’ domain. The corrector steps are based on quadratic subprograms that combine aspects of line search and trust region methods. Convergence results are given, and some preliminary numerical experiments suggest a high robustness of the proposed method.