In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transpor...

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution another problem. As consequence, bilevel able model hierarchical decision processes. This appealing for modeling real-world problems, but it also makes resulting models hard solve theory and practice. The scientific interest computational increased lot over last decade still gr...

This paper presents a bilevel programming formulation of a leader±follower game that can be used to help decision makers arrive at a rational policy for encouraging biofuel production. In the model, the government is the leader and would like to minimize the annual tax credits it allows the petro-chemical industry for producing biofuels. The crops grown for this purpose are on land now set asid...

One of the most fundamental problems in model predictive control (MPC) is the lack of guaranteed stability and feasibility. It is shown how Farkas’ Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC controller. Alternatively, the method can be us...

We provide a global heuristic for a class of bilevel programs with bilinear objectives and linear contraints. The algorithm relies on an interior point approach that can be seen as a combination of the smoothing and implicit programming techniques wellknown in the MPEC literature. But contrary to what is usually done, here the focus is on global optimality. We tested the algorithm on large-scal...

We propose to solve generalized bilevel programs by a trust region approach where the “model” takes the form of a bilevel program involving a linear program at the upper level and a linear variational inequality at the lower level. By coupling the concepts of trust region and linesearch in a novel way, we obtain an implementable algorithm that converges to a strong stationary point of the origi...

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for computing efficiently local minimizers. The method is based on the given structural analysis and combines i...