Exact penalty functions for nonlinear integer programming problems
type: Item
instance of: scholarly article
title: Exact penalty functions for nonlinear integer programming problems
zbMATH Open document ID: 1206.90100
published in: Journal of Optimization Theory and Applications
publication date: 2010-07-24T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: The authors first find a set of sufficient conditions under which the nonlinear problem \(\min \{ f(x) \, : \, x\in W \}\) has the same minimum point(s) as each member of the family \(\min \{ f(x)+\phi (x, \varepsilon) \, : \, x\in X \}\) (\(0<\varepsilon < \overline{\varepsilon} \)). Here \(W\subseteq X \subseteq \mathbb R ^n\), \(f,\phi (\cdot , \varepsilon) : \mathbb R ^n\longrightarrow \mathbb R\) and \(\overline{\varepsilon} \) is a positive number, depending on \(W\), \(X\), \(f\), and \(\phi\). Then they provide 6 explicit penalty terms \(\phi (\cdot, \varepsilon)\) in case \(W\subseteq \{ 0,1 \}^n\), and 2 additional ones valid for a general integer programming problem.
reviewed by: Mihai Cipu
Mathematics Subject Classification ID: 90C10
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 5760462
zbMATH Keywords: nonlinear integer programming
zbMATH Keywords: continuous programming
zbMATH Keywords: exact penalty functions
author: Stefano Lucidi
author: F. Rinaldi
MaRDI profile type: Publication
OpenAlex ID: W2094034289
cites work: Finding independent sets in a graph using continuous multivariable polynomial formulations.
cites work: Constructing test functions for global optimization using continuous formulations of graph problems
cites work: Introduction to global optimization.
cites work: Knapsack feasibility as an absolute value equation solvable by successive linear programming
cites work: An algorithm for nonlinear optimization problems with binary variables
cites work: Q5494211
cites work: Topics in semidefinite and interior-point methods
cites work: On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints
cites work: An exact penalty approach for solving a class of minimization problems with boolean variables
cites work: Q4110818
cites work: Penalty for zero–one integer equivalent problem
cites work: Penalty formulation for zero-one nonlinear programming
cites work: New results on the equivalence between zero-one programming and continuous concave programming
cites work: Penalty parameter for linearly constrained 0--1 quadratic programming
DOI: 10.1007/S10957-010-9700-7
description: scientific article; zbMATH DE number 5760462