Conjugate points for a constrained nonlinear programming problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 0983.49014
author: Hidefumi Kawasaki
publication date: 2001-11-27T00:00:00Z
Mathematics Subject Classification ID: 49K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 1588149
zbMATH Keywords: conjugate points
zbMATH Keywords: strict conjugate points
zbMATH Keywords: Jacobi equation
zbMATH Keywords: Legendre condition
zbMATH Keywords: positive definite
zbMATH Keywords: shortest path problem
zbMATH Keywords: Sylvester's criterion
zbMATH Keywords: principal minors
MaRDI profile type: Publication
title: Conjugate points for a constrained nonlinear programming problem
published in: Journal of Nonlinear and Convex Analysis
review text: In a former paper by the author, the notion of conjugate point for unconstrained finite dimensional optimization problems was introduced. This notion is based on the discretized version of the Jacobi equation related to the second-order Hessian matrix of the objective function. The aim of this paper is to extend this theory to the inequality-equality constrained situation and offer necessary and sufficient conditions of optimality for such programming problems. As an illustration, the finite-dimensional version of the shortest path problem on the unit sphere is analyzed.
reviewed by: Zsolt Páles
description: scientific article