Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm

In this paper, we present an original method to solve convex bilevel programming problems in an optimistic approach. Both upper and lower level objective functions are convex and the feasible region is a polyhedron. The enumeration sequential linear programming algorithm uses primal and dual monoton...

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Veröffentlicht in:Journal of global optimization Jg. 47; H. 4; S. 615 - 637
1. Verfasser: Etoa, Jean Bosco Etoa
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.08.2010
Springer Nature B.V
Schlagworte:
Algorithms
Computer Science
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Studies
Variables
Convex quadratic bilevel program
Primal-dual monotonicity
Monotonicity network
Enumeration sequential quadratic programming algorithm
ISSN:0925-5001, 1573-2916
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Zusammenfassung:In this paper, we present an original method to solve convex bilevel programming problems in an optimistic approach. Both upper and lower level objective functions are convex and the feasible region is a polyhedron. The enumeration sequential linear programming algorithm uses primal and dual monotonicity properties of the primal and dual lower level objective functions and constraints within an enumeration frame work. New optimality conditions are given, expressed in terms of tightness of the constraints of lower level problem. These optimality conditions are used at each step of our algorithm to compute an improving rational solution within some indexes of lower level primal-dual variables and monotonicity networks as well. Some preliminary computational results are reported.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-009-9482-3