A penalty function method for solving weak price control problem
type: Item
instance of: scholarly article
title: A penalty function method for solving weak price control problem
zbMATH Open document ID: 1118.65063
author: Yibing Lv
author: Tiesong Hu
author: Zhongping Wan
published in: Applied Mathematics and Computation
publication date: 2007-06-06T00:00:00Z
review text: The authors are concerned with a class of weak price control problems, which is an important linear bilevel programming problem with non-unique lower level solutions. In order to explore the existence of an optimal solution, the weak price control problem is transformed into the corresponding penalized problem, which is a quadratic programming problem. Then the relationship between the solutions of the weak price control problem and the corresponding penalized problem is established. Based on the theoretical results a simple algorithm to solve the weak price control problem is given and the convergence of the proposed algorithm is analysed. A numerical example shows that the algorithm is feasible and efficient.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 5162007
zbMATH Keywords: linear bilevel programming
zbMATH Keywords: duality
zbMATH Keywords: penalty method
zbMATH Keywords: quadratic programming
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: j.amc.2006.07.151
OpenAlex ID: W1988719199
cites work: Computational Difficulties of Bilevel Linear Programming
cites work: On two-level optimization
cites work: Foundations of bilevel programming
cites work: Weak linear bilevel programming problems: existence of solutions via a penalty method
cites work: A solution method for the linear static Stackelberg problem using penalty functions
cites work: On the definition of linear bilevel programming solution
DOI: 10.1016/J.AMC.2006.07.151
description: scientific article; zbMATH DE number 5162007