A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints
type: Item
instance of: scholarly article
title: A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints
zbMATH Open document ID: 0966.65052
author: Thomas F. Coleman
author: Yuying Li
published in: Mathematical Programming. Series A. Series B
publication date: 2001-08-21T00:00:00Z
review text: A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints. A Newton step is derived from the complementarity conditions. Based on this Newton step, a trust region subproblem is formed and the original objective function is monotonically decreased. Explicit sufficient decrease conditions are proposed for satisfying the first-order and second-order necessary conditions. There are global and local convergence properties of the proposed trust region and affine scaling interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfying complementarity, dual feasibility and second-order necessary conditions, respectively. It is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem.
reviewed by: Stefan Mititelu
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 1546855
zbMATH Keywords: nonconvex minimization
zbMATH Keywords: nonlinear programming
zbMATH Keywords: trust region method
zbMATH Keywords: affine scaling
zbMATH Keywords: interior point method
zbMATH Keywords: linear inequality constraints
zbMATH Keywords: convergence
describes a project that uses: TRICE
MaRDI profile type: Publication
DOI: 10.1007/S101070000139
description: scientific article; zbMATH DE number 1546855