A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

Abstract

In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality conditions are derived. They are based on the notion of equilibrium point of an exact penalization for LBP. It is described how an equilibrium point can be obtained with the simplex method. It is shown that the information in the simplex tableaux can be used to get necessary and sufficient local optimality conditions for LBP. Based on these conditions, a simplex type algorithm is proposed, which attains a local solution of LBP by moving in equilibrium points. A numerical example illustrates how the algorithm works. Some computational results are reported.

A Bilevel Quadratic–Quadratic Fractional Programming through Fuzzy Goal Programming approach

“…The idea of bilevel programming problems was firstly introduced by a Candler and Townsley [2] as well as by Fortuni-Amat and McCarl [4]. Many researchers have designed algorithms for the solution of the BLPP [10, [11], [17], [20], [34]. Amat and McCarl [4] presented the formal formulation of BLPP.…”