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An Interior Method for Nonconvex Semidefinite Programs

Jarre, Florian

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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An Interior Method for Nonconvex Semidefinite Programs

Jarre, Florian

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.

An Interior Method for Nonconvex Semidefinite Programs

Jarre, Florian

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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Title:

An Interior Method for Nonconvex Semidefinite Programs

Contributors:

Jarre, Florian (author)

Published in:

Optimization and Engineering ; 1 ; 347-372

Publication date:

2000-12-01

Size:

26 pages

ISSN:

1573-2924 , 1389-4420

DOI:

https://doi.org/10.1023/A:1011562523132

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

nonlinear optimization , semidefinite program , predictor corrector method , trust region method Mathematics , Agriculture , Systems Theory, Control , Optimization , Engineering, general , Environmental Management , Operation Research/Decision Theory

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