Pessimistic bilevel linear optimization
نویسندگان
چکیده
In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.
منابع مشابه
Easier than We Thought – A Practical Scheme to Compute Pessimistic Bilevel Optimization Problem
In this paper, we present a new computation scheme for pessimistic bilevel optimization problem, which so far does not have any computational methods generally applicable yet. We first develop a tight relaxation and then design a simple scheme to ensure a feasible and optimal solution. Then, we discuss using this scheme to compute linear pessimistic bilevel problem and several variants. We also...
متن کاملMethods for solving the bilevel optimization problems
1. Introduction. Nowadays, the bilevel optimization problems, arising in various applications [1, 2], seem to be one of the most attractive fields for many experts [1, 3, 4, 5]. Bilevel problems are such optimization problems, which – side by side with ordinary constraints such as equalities and inequalities [6] – include a constraint described as an optimization subproblem, called the lower-le...
متن کاملPessimistic Referential-Uncooperative Linear Bilevel Multi-follower Decision Making with An Application to Water Resources Optimal Allocation
Abstract: In this paper, we study a pessimistic linear bilevel multi-follower programming problem in a referential-uncooperative situation (for short, PLBMF-RU) where the followers are uncooperative while having cross reference to decision making information of the other followers. We first give a model and the solution definitions of PLBMF-RU, and then use a simple example to illustrate it. Fu...
متن کاملPessimistic Bilevel Optimization
We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on probl...
متن کاملBILEVEL LINEAR PROGRAMMING WITH FUZZY PARAMETERS
Bilevel linear programming is a decision making problem with a two-level decentralized organization. The textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. Making a decision at one level affects that at the other one. In this paper, bilevel linear programming with inexact parameters has been studied and a method is...
متن کامل