Methods of embedding-cutting off in problems of mathematical programming
type: Item
instance of: scholarly article
title: Methods of embedding-cutting off in problems of mathematical programming
zbMATH Open document ID: 1229.90134
author: Valerian Bulatov
published in: Journal of Global Optimization
publication date: 2010-10-06T00:00:00Z
review text: The author considers general iterative embedding procedures for finding a global minimizer of a continuous real-valued function on a compact subset of the \(n\)-dimensional Euclidean space. In particular a cutting type procedure is studied for inequality constrained problems for which the variables stay in a compact set and the objective function and the constraint functions have concave minorants. The latter is particularly true when the functions are linear, convex, or concave. As an example of the procedure a specific cutting plane method is investigated which is suitable for the solution of small-dimensional problems with linear inequality constraints and lower and upper bounds on the variables. Particular attention is devoted to the case that the objective function of the problem is concave. The cutting plane method is tested on some randomly generated quadratic functions with an indefinite matrix and up to 10 variables.
reviewed by: Rembert Reemtsen
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 5796470
zbMATH Keywords: global optimization
zbMATH Keywords: concave minorant
zbMATH Keywords: cutting plane
zbMATH Keywords: nondegenerate matrix
zbMATH Keywords: section plane
zbMATH Keywords: second-order cut
MaRDI profile type: Publication
full work available at URL: s10898-009-9523-y
OpenAlex ID: W1995580004
cites work: Q5652462
cites work: On stability and stationary points in nonlinear optimization
cites work: Q4302075
cites work: Q3972966
cites work: Q3997222
cites work: The Cutting-Plane Method for Solving Convex Programs
cites work: Q3908420
cites work: Cutting-Plane Methods without Nested Constraint Sets
cites work: The Supporting Hyperplane Method for Unimodal Programming
cites work: Nonlinear Programming: A Numerical Survey
DOI: 10.1007/S10898-009-9523-Y
description: scientific article; zbMATH DE number 5796470