An Interior Method for Nonconvex Semidefinite Programs |
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Authors: | Jarre Florian |
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Affiliation: | (1) Institut für Mathematik, Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany |
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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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Keywords: | nonlinear optimization semidefinite program predictor corrector method trust region method |
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