An Interior Point Constrained Trust Region Method for a Special Class of Nonlinear Semidefinite Programming Problems

In this paper, an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming (SDP) problems is described and analyzed. Such nonlinear and nonconvex programs arise, e.g., in the design of optimal static or reduced order output feedback control laws and hav...

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Vydáno v:SIAM journal on optimization Ročník 12; číslo 4; s. 1048 - 1074
Hlavní autoři: Leibfritz, F., Mostafa, E. M. E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 2002
Témata:
Algorithms
Applied mathematics
Control theory
Decomposition
Methods
Optimization
Quadratic programming
Semidefinite programming
Variables
ISSN:1052-6234, 1095-7189
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Shrnutí:In this paper, an interior point trust region algorithm for the solution of a class of nonlinear semidefinite programming (SDP) problems is described and analyzed. Such nonlinear and nonconvex programs arise, e.g., in the design of optimal static or reduced order output feedback control laws and have the structure of abstract optimal control problems in a finite dimensional Hilbert space. The algorithm treats the abstract states and controls as independent variables. In particular, an algorithm for minimizing a nonlinear matrix objective functional subject to a nonlinear SDP-condition, a positive definiteness condition, and a nonlinear matrix equation is considered. The algorithm is designed to take advantage of the structure of the problem. It is an extension of an interior point trust region method to nonlinear and nonconvex SDPs, with a special structure which applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure robustness of the iteration. Some convergence results are given, and, finally, several numerical examples demonstrate the applicability of the considered algorithm.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623400375865