In this paper we use bilevel programming to find the maximum difference between a model predictive controller (MPC) using a full model and an MPC using a reduced model. The results apply to MPC with quadratic cost function and linear model with linear constraints.

In this paper we study the bilevel linear programming problem with multiple objective functions at the upper level, with particular focus on the bi-objective case. We examine some properties of this problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem. The basic idea consists in applying a reference poin...

Basic bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his/her objective, subject to a set of constraints and his/her follower’s solution, and the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. Three issues may be involved in a basic bilevel d...

In this paper, we consider the bilevel linear programming problem (BLPP) where all coefficients in are interval type-2 triangular fuzzy numbers (IT2TFNs). First, convert a BLPP with IT2TFN parameters to an BLPP. next step, solve BLPPs and obtain optimal solution as IT2TFN.

I In this paper, we propose an algorithm base on decomposition technique for solving the mixed integer linear multiplicative-linear bilevel problems. In fact, this algorithm is an application of the algorithm given by G. K. Saharidis et al for the case in which the first level objective function is linear multiplicative. We use properties of quasi-concave of bilevel programming problems and dec...

We consider the bilevel uncapacitated facility location problem with user preferences. It is known that this model may be reformulated as a one-level location problem with some additional constraints. In this paper we introduce a new reformulation and show that this reformulation dominates three previous ones from the point of view of their linear programming relaxations and may be worse than a...

This paper is an extension of the K th-best approach [4] for solving bilevel linear programming problems with integer variables. NAZ cut [2] and A-T cut [3] are added to reach the integer optimum. An example is given to show the efficiency of the proposed algorithm.