On the penalization method in mathematical programming
type: Item
instance of: scholarly article
title: On the penalization method in mathematical programming
zbMATH Open document ID: 0886.90131
published in: Doklady Mathematics
publication date: 1998-01-05T00:00:00Z
review text: Well known in mathematical programming (MP) are the techniques of equivalent and asymptotic reduction of constrained optimization problems to unconstrained ones, more precisely, to problems in which any part of the original constraints is accumulated by a modified objective function. These techniques are of fundamental importance: they not only generate new methods for solving optimization problems but are the basis for many theoretical principles of MP, for example, optimality conditions, modified Lagrange functions, duality for improper problems in MP, and other. Such techniques continue to attract interest. We first state some equivalence theorems, give estimates of the constraint residuals and then apply the penalization method to (1) the problem of sequential correction of an improver linear programming problem of the first kind, (2) the problem of sequential Pareto correction of an improper problem of piecewise linear programming. Finally we discuss the nondifferentiability of the penalty function as a necessary condition for equivalent reduction. All results are stated without proofs.
reviewed by: Norbert Heldermann
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M30
zbMATH DE Number: 1099477
zbMATH Keywords: equivalence theorems
zbMATH Keywords: estimates of the constraint residuals
zbMATH Keywords: penalization method
zbMATH Keywords: sequential correction of an improver linear programming
zbMATH Keywords: sequential Pareto correction
zbMATH Keywords: piecewise linear programming
zbMATH Keywords: nondifferentiability
author: Ivan I. Eremin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1099477