Polynomial convergence of second-order mehrotra-type predictor-corrector algorithms over symmetric cones
type: Item
instance of: scholarly article
title: Polynomial convergence of second-order mehrotra-type predictor-corrector algorithms over symmetric cones
zbMATH Open document ID: 1268.90128
author: Xinze Liu
author: Changhe Liu
author: Hongwei Liu
published in: Journal of Optimization Theory and Applications
publication date: 2013-02-11T00:00:00Z
review text: This article considers the linear programming problem on a symmetric cone. The paper begins with a description of Euclidean Jordan algebras, symmetric cones and their properties, followed by the interior-point method that produces a second-order Mehrota-type predictor-corrector algorithm. The proposed algorithm includes adaptive updates of a centering parameter. The last section considers complexity issues and the polynomial convergence of the algorithm.
reviewed by: Efstratios Rappos
Mathematics Subject Classification ID: 90C51
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 6135487
zbMATH Keywords: symmetric cone
zbMATH Keywords: Euclidean Jordan algebra
zbMATH Keywords: interior-point methods
zbMATH Keywords: second-order methods
zbMATH Keywords: Mehrotra-type algorithm
zbMATH Keywords: polynomial complexity
MaRDI profile type: Publication
full work available at URL: s10957-012-0018-5
OpenAlex ID: W1989801777
cites work: Q4321748
cites work: Self-Scaled Barriers and Interior-Point Methods for Convex Programming
cites work: Primal-Dual Interior-Point Methods for Self-Scaled Cones
cites work: Barrier Functions in Interior Point Methods
cites work: Linear systems in Jordan algebras and primal-dual interior-point algorithms
cites work: Euclidean Jordan algebras and interior-point algorithms
cites work: A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite 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: 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: A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming
cites work: Extension of primal-dual interior point algorithms to symmetric cones
cites work: The \(Q\) method for symmetric cone programming
cites work: Full Nesterov-Todd step infeasible interior-point method for symmetric optimization
cites work: An Infeasible Interior Point Method for Linear Complementarity Problems over Symmetric Cones
cites work: Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric Cones
cites work: Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones.
cites work: Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming
cites work: On the Implementation of a Primal-Dual Interior Point Method
cites work: On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms
cites work: Polynomial time second order mehrotra-type predictor--corrector algorithms
cites work: On Mehrotra-Type Predictor-Corrector Algorithms
cites work: On the complexity analysis of a Mehrotra-type primal–dual feasible algorithm for semidefinite optimization
cites work: Q5691079
DOI: 10.1007/S10957-012-0018-5
description: scientific article; zbMATH DE number 6135487