Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm
type: Item
instance of: scholarly article
title: Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm
zbMATH Open document ID: 1237.90176
author: Jean Bosco Etoa Etoa
published in: Journal of Global Optimization
publication date: 2010-10-06T00:00:00Z
review text: The author proposes an enumeration sequential quadratic programming algorithm to solve convex bilevel programming problems in an optimistic approach. The upper and lower level objective functions are convex and the feasible region is a polyhedron. From monotonicity principles a new concept of monotonicity networks is introduced. A monotonicity path is used to express the tightness of some subsets of the primal and dual lower level constraints, depending on the current rational solution. At each step of the algorithm, monotonicity paths are used to compute an improving rational solution within the tightness of primal-dual lower level constraints. Given a feasible or rational solution in a branch and bound framework, the method performs a sequential investigation on some indexes of lower level primal-dual variables in order to compute some improved rational solutions.
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C55
zbMATH DE Number: 5796458
zbMATH Keywords: convex bilevel program
zbMATH Keywords: enumeration sequential quadratic programming algorithm
zbMATH Keywords: primal-dual monotonicity
reviewed by: Maxim Ivanov Todorov
MaRDI profile type: Publication
full work available at URL: s10898-009-9482-3
OpenAlex ID: W2058401669
cites work: Government-private sector relations as a Stackelberg game. A degenerate case
cites work: Links between linear bilevel and mixed 0-1 programming problems
cites work: A Branch and Bound Algorithm for the Bilevel Programming Problem
cites work: Convex two-level optimization
cites work: Optimality conditions for the bilevel programming problem
cites work: A bilevel programming approach to determining tax credits for biofuel production
cites work: Computational Difficulties of Bilevel Linear Programming
cites work: Q5602534
cites work: Two-Level Linear Programming
cites work: A bilevel model and solution algorithm for a freight tariff-setting problem
cites work: On the quasiconcave bilevel programming problem
cites work: A note on a penalty function approach for solving bilevel linear programs
cites work: The nonlinear bilevel programming problem:formulations,regularity and optimality conditions
cites work: Bilevel programming: a survey
cites work: A simple algorithm for the-linear bilevel programming problem
cites work: A necessary and a sufficient optimality condition for bilevel programming problems
cites work: Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
cites work: On the Accurate Identification of Active Constraints
cites work: On bilevel programming. I: General nonlinear cases
cites work: Filled functions for unconstrained global optimization.
cites work: New Branch-and-Bound Rules for Linear Bilevel Programming
cites work: The polynomial hierarchy and a simple model for competitive analysis
cites work: Derivative evaluation and computational experience with large bilevel mathematical programs
cites work: Two-Level Planning
cites work: A bilevel model of taxation and its application to optimal highway pricing
cites work: Hybrid approach with active set identification for mathematical programs with complementarity constraints
cites work: An Algorithm for the Traveling Salesman Problem
cites work: Q5717956
cites work: A global optimization method for solving convex quadratic bilevel programming problems
cites work: Convex Analysis
cites work: The steepest descent direction for the nonlinear bilevel programming problem
cites work: Linear bilevel problems: genericity results and an efficient method for computing local minima
cites work: Bilevel and multilevel programming: A bibliography review
cites work: Descent approaches for quadratic bilevel programming
cites work: A hierarchical optimization model of resource allocation
DOI: 10.1007/S10898-009-9482-3
description: scientific article; zbMATH DE number 5796458