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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Vydané v:	Journal of global optimization Ročník 47; číslo 4; s. 615 - 637
Hlavný autor:	Etoa, Jean Bosco Etoa
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Boston Springer US 01.08.2010 Springer Nature B.V
Predmet:	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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Abstract	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.
AbstractList	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.[PUBLICATION ABSTRACT] 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.
Author	Etoa, Jean Bosco Etoa
Author_xml	– sequence: 1 givenname: Jean Bosco Etoa surname: Etoa fullname: Etoa, Jean Bosco Etoa email: jbetoa_etoa@hotmail.com, jbetoa3101@rogers.com organization: Department of Economic and Management Sciences, University of Yaounde II, Cameroon High Commission
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Snippet	In this paper, we present an original method to solve convex bilevel programming problems in an optimistic approach. Both upper and lower level objective...
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SubjectTerms	Algorithms Computer Science Linear programming Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Quadratic programming Real Functions Studies Variables
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Title	Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm
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