Taylor Approach for Solving Non-Linear Bi-level Programming Problem

Eghbal Hosseini, Isa Nakhai Kamalabadi


In recent years the bi-level programming problem (BLPP) is interested by many researchers and it is known as an appropriate tool to solve the real problems in several areas such as computer science, engineering, economic, traffic, finance, management and so on. Also it has been proved that the general BLPP is an NP-hard problem. The literature shows a few attempts for using approximate methods. In this paper we attempt to develop an effective approach based on Taylor theorem to obtain an approximate solution for the non-linear BLPP. In this approach using the Karush-Kuhn–Tucker, the BLPP has been converted to a non-smooth single problem, and then it is smoothed by the Fischer – Burmeister function. Finally the smoothed problem is solved using an approach based on Taylor theorem. The presented approach achieves an efficient and feasible solution in an appropriate time which has been is evaluated by comparing to references and test problems.


Non-linear bi-level programming problem; Taylor theorem; Karush-Kuhn–Tucker conditions; smoothing methods

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