A SURVEY OF NUMERICAL METHODS FOR NONLINEAR SEMIDEFINITE PROGRAMMING

A SURVEY OF NUMERICAL METHODS FOR NONLINEAR SEMIDEFINITE PROGRAMMING

Nonlinear semidefinite programming (SDP) problems have received a lot of attentions because of large variety of applications. In this paper, we survey numerical methods for solving nonlinear SDP problems. Three kinds of typical numerical methods are described; augmented Lagrangian methods, sequentia...

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Veröffentlicht in:Journal of the Operations Research Society of Japan 2015, Vol.58(1), pp.24-60
Hauptverfasser: Yamashita, Hiroshi, Yabe, Hiroshi
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
augmented Lagrangian method
Convergence
Mathematical problems
Mathematical programming
nonlinear semidefinite programming
Numerical analysis
Numerical methods
Optimization
primal-dual interior point method
Semidefinite programming
sequential SDP method
Studies
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Zusammenfassung:Nonlinear semidefinite programming (SDP) problems have received a lot of attentions because of large variety of applications. In this paper, we survey numerical methods for solving nonlinear SDP problems. Three kinds of typical numerical methods are described; augmented Lagrangian methods, sequential SDP methods and primal-dual interior point methods. We describe their typical algorithmic forms and discuss their global and local convergence properties which include rate of convergence.
ISSN:0453-4514
2188-8299
1878-6871
DOI:10.15807/jorsj.58.24