An interior method for nonconvex semidefinite programs

An interior method for nonconvex semidefinite programs

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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:
Abstract:

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.

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