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2013•Numerical Functional Analysis and OptimizationRequires access

An Objective Penalty Function Algorithm for Bilevel Programming Based on Multi-Parameters

Zhiqing Meng, Xinsheng Xu, Rui Shen, Min Jiang

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Abstract

In this article, an objective penalty function algorithm based on multi-parameters is proposed for solving bilevel programming convex to the lower level problem. Under some conditions, an optimal solution to a single-objective programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. We prove that the algorithm is convergent under some conditions. Numerical results show that the algorithm is efficient for solving some bilevel programming convex to the lower level problem.

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What this paper is about

In this article, an objective penalty function algorithm based on multi-parameters is proposed for solving bilevel programming convex to the lower level problem. Under some conditions, an optimal solution to a single-objective programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. We prove that the algorithm is convergent under some conditions. Numerical results show that the algorithm is efficient for solving some bilevel programming convex to the lower level problem.

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Available abstract

In this article, an objective penalty function algorithm based on multi-parameters is proposed for solving bilevel programming convex to the lower level problem. Under some conditions, an optimal solution to a single-objective programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. We prove that the algorithm is convergent under some conditions. Numerical results show that the algorithm is efficient for solving some bilevel programming convex to the lower level problem.

Key concepts: Bilevel optimization, Penalty method, Mathematical optimization, Mathematics, Regular polygon, Function (biology), Convex optimization, Algorithm

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