We consider a bilevel road pricing problem. The lower level models a traffic assignment problem, whereas the upper level represents a toll problem which has impact on the distribution of the users on the network. We investigate the structure of this problem and consider a special lower level objective function. We show that a solution algorithm [10] can be applied to the optimal value reformula...

The principal challenge in inventory control in supply chains consists of planning for a set of autonomous enterprises under information asymmetry and disparate, potentially conflicting objectives. In this paper, we investigate four different computational approaches to cope with this challenge: the decomposition, the integrated, the coordinated, and the bilevel programming approaches. Beyond t...

We propose a new solving approach for shape optimization (optimal design problem) of elastic solids in contact. As the equilibrium of a solid in contact is a solution of constrained minimization problem for the body energy functional (or an variational inequality), we can consider our optimization problem as a classical bilevel mathematical program (or a generalized bilevel programming problem)...

Bilevel programs are optimization problems which have a subset of their variables constrained to be an optimal solution of another problem parameterized by the remaining variables. They have been applied to decentralized planning problems involving a decision process with a hierarchical structure. This paper considers the linear fractional/quadratic bilevel programming (LFQBP) problem, in which...

The generalized bilevel programming problem (GBLP) is a bilevel mathematical program where the lower level is a variational inequality. In this paper we prove that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decision variable, then using certain uniform parametric error bounds as penalty functions giv...

The bilevel program is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. The classical approach to solving such a problem is to replace the lower level problem by its Karush–Kuhn–Tucker (KKT) condition and solve the resulting mathematical programming problem with equilibrium con...

This paper contains a bibliography of all references central to bilevel and mul-tilevel programming that the authors know of. It should be regarded as a dynamic and permanent contribution since, all the new and appropriate references that are brought to our attention will be periodically added to this bibliography. Readers are invited to suggest such additions, as well as corrections or modiica...

This paper considers a bilevel programming approach to applying coherent risk measures to extended two-stage stochastic programming problems. This formulation technique avoids the time-inconsistency issues plaguing naive models and the incomposability issues which cause time-consistent formulations to have complicated, hard-to-explain objective functions. Unfortunately, the analysis here shows ...

In this article, we compare two different calmness conditions which are widely used in the literature on bilevel programming and on mathematical programs with equilibrium constraints. In order to do so, we consider convex bilevel programming as a kind of intersection between both research areas. The so-called partial calmness concept is based on the function value approach for describing the lo...

An improved particle swarm optimization PSO algorithm is proposed for solving bilevel multiobjective programming problem BLMPP . For such problems, the proposed algorithm directly simulates the decision process of bilevel programming, which is different from most traditional algorithms designed for specific versions or based on specific assumptions. The BLMPP is transformed to solvemultiobjecti...