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A GLOBAL CONVERGENT METHOD FOR NONLINEAR BILEVEL PROGRAMMING PROBLEM

Yabo Zheng, Zhongping Wan, Yibing Lv

Open publisher page 2 citations

Abstract

In this paper,we consider a nonlinear bilevel programming problem in which the lower level is a linear programming problem.By using the dual theory,the original problem is transformed into a single level optimization program.Then,we construct a penalized problem by using the duality gap of the lower level problem as a penalty parameter.Furthermore,we obtain a global solution of the nonlinear bilevel programming problem.Finally,some numerical results show that the proposed method is feasible.

About this research paper

What this paper is about

In this paper,we consider a nonlinear bilevel programming problem in which the lower level is a linear programming problem.By using the dual theory,the original problem is transformed into a single level optimization program.Then,we construct a penalized problem by using the duality gap of the lower level problem as a penalty parameter.Furthermore,we obtain a global solution of the nonlinear bilevel programming problem.Finally,some numerical results show that the proposed method is feasible.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper,we consider a nonlinear bilevel programming problem in which the lower level is a linear programming problem.By using the dual theory,the original problem is transformed into a single level optimization program.Then,we construct a penalized problem by using the duality gap of the lower level problem as a penalty parameter.Furthermore,we obtain a global solution of the nonlinear bilevel programming problem.Finally,some numerical results show that the proposed method is feasible.

Key concepts: Bilevel optimization, Mathematical optimization, Nonlinear programming, Nonlinear system, Duality (order theory), Dual (grammatical number), Mathematics, Linear programming

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