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Title: An interior point method for semidefinite programming

Semidefinite programming is of rising importance in min-max eigenvalue problems and relaxations for NP-complete problems. We present a new interior point algorithm based on the linearization XZ {minus} {mu}I which is very successful in linear programming. We show that, although the original {Delta}X is not symmetric, by using the symmetric part of {Delta}X convergence can be guaranteed. The algorithm works for arbitrary combinations of equalities and inequalities and, contrary to linearizations such as XZ + ZX {minus} {mu}I, does not make use of Kronecker products. In numerical experiments the algorithm exhibits fast quadratic convergence.
Authors:
; ; ;
Publication Date:
OSTI Identifier:
36122
Report Number(s):
CONF-9408161-
TRN: 94:009753-0397
Resource Type:
Conference
Resource Relation:
Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
Publisher:
Univ. of Michigan, Ann Arbor, MI (United States)
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; MATRICES; NONLINEAR PROGRAMMING; ALGORITHMS