Piecewise convex approach to a family of nonconvex problems with applications in supply optimization

Ider Tseveendorj
Department of mathematics
University of Orleans, France
ider.tseveendorj@labomath.univ-orleans.fr

Dominique Fortin,
INRIA-Rocquencourt, France
Dominique.Fortin@inria.fr

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In problems of pricing, reactions of clients play an important role in the total revenue of the decision maker. Such kind of problem could be formulated as a mathematical program with equilibrium constraints or as a bilevel optimization problem.  Then one could reformulate it as a nonlinear programming problem. The result is a highly nonconvex optimization problem.  It is computationally difficult to solve, especially one wishes to compute a globally optimal revenue. We will present an approach based on approximating objective function of the problem obtained by piecewise convex functions and on solving sequential  piecewise convex maximization problems.  For the later we propose global optimality conditions and an algorithm.

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