On a commutative class of search directions for linear programming over symmetric cones
type: Item
instance of: scholarly article
title: On a commutative class of search directions for linear programming over symmetric cones
zbMATH Open document ID: 0994.90095
DOI: 10.1023/A:1017920200889
author: R. Smith
published in: Journal of Optimization Theory and Applications
publication date: 2002-06-09T00:00:00Z
review text: The author investigates the complexity of rather general path-following techniques for linear programming problems over symmetric cones. In particular, a commutative class of search directions is studied. As abstract tool the author uses the approach given in the book \textit{J. Faraut} and \textit{A. Korányi} [Analysis on symmetric cones. Clarendon Press, Oxford (1994; Zbl 0841.43002)]. A study of it is recommended to be easier able to follow the applied concept of Euclidean Jordan algebra and Pierce decomposition.
reviewed by: Christian Grossmann
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 1752505
zbMATH Keywords: Symmetric cones
zbMATH Keywords: primal-dual interior point methods
zbMATH Keywords: Euclidean Jordan algebra
zbMATH Keywords: complexity
MaRDI profile type: Publication
cites work: A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming
cites work: Primal-Dual Interior-Point Methods for Self-Scaled Cones
cites work: Linear systems in Jordan algebras and primal-dual interior-point algorithms
cites work: Similarity and other spectral relations for symmetric cones
cites work: Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones.
cites work: Primal--Dual Path-Following Algorithms for Semidefinite Programming
cites work: On Extending Some Primal--Dual Interior-Point Algorithms From Linear Programming to Semidefinite Programming
cites work: Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions
cites work: A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming
cites work: An Interior-Point Method for Semidefinite Programming
cites work: Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices
cites work: Q4321748
cites work: Q4327459
cites work: A long-step primal--dual algorithm for the symmetric programming problem
full work available at URL: a:1017920200889
OpenAlex ID: W1543242366
description: scientific article; zbMATH DE number 1752505