Successive Linearization Methods for Nonlinear Semidefinite Programs

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint....

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Bibliographic Details
Published in:Computational optimization and applications Vol. 31; no. 3; pp. 251 - 273
Main Authors: Kanzow, Christian, Nagel, Christian, Kato, Hirokazu, Fukushima, Masao
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.07.2005
Subjects:
Algorithms
Applied mathematics
Control theory
Convergence
Globalization
Iterative methods
Linearization
Mathematical analysis
Mathematical models
Matrix methods
Methods
Nonlinear programming
Optimization
Software
Studies
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-005-3231-4