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

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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.

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Author notes

  1. Jean Bosco Etoa Etoa

    Present address: Cameroon High Commission, 170 Clemow Avenue, Ottawa, ON, K1S 2B4, Canada

Authors and Affiliations

  1. Department of Economic and Management Sciences, University of Yaounde II, BP 15, Soa, Yaounde, Cameroon

    Jean Bosco Etoa Etoa

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  1. Jean Bosco Etoa Etoa
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Correspondence to Jean Bosco Etoa Etoa.

Additional information

The algorithm presented in this paper was conceived during a PhD research program of the author at MAGI, École Polytechnique de Montréal, C. P. 6079, succ. Centre-ville Montréal (Québec), H3C 3A7 Canada [21].

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Etoa, J.B.E. Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm. J Glob Optim 47, 615–637 (2010). https://doi.org/10.1007/s10898-009-9482-3

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