A HYBRID ALGORITHM FOR OPTIMIZING EIGENVALUES OF SYMMETRICAL DEFINITE PENCILS

被引：8

作者：

HAEBERLY, JPA ^{[1
]}

OVERTON, ML ^{[1
]}

机构：

[1] NYU,COURANT INST MATH SCI,DEPT COMP SCI,NEW YORK,NY 10012

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1994年 / 15卷 / 04期

关键词：

NONSMOOTH OPTIMIZATION; GENERALIZED EIGENVALUE PROBLEM; MATRIX PENCIL; LYAPUNOV EQUATIONS;

D O I：

10.1137/S0895479893244833

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm is presented for the optimization of the maximum eigenvalue of a symmetric definite pencil depending affinely on a vector of parameters. The algorithm uses a hybrid approach, combining a scheme based on the method of centers, developed by Boyd and El Ghaoui [Linear Algebra Appl., 188 (1993), pp. 63-1121, with a new quadratically convergent local scheme. A convenient expression for the generalized gradient of the maximum eigenvalue of the pencil is also given, expressed in terms of a dual matrix. The algorithm computes the dual matrix that establishes the optimality of the computed solution.

引用

页码：1141 / 1156

页数：16

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