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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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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DOI: https://doi.org/10.1007/s10898-009-9482-3