An Objective Penalty Function of Bilevel Programming

Zhiqing Meng (), Chuangyin Dang (), Rui Shen () and Ming Jiang ()
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Zhiqing Meng: Zhejiang University of Technology
Chuangyin Dang: City University of Hong Kong
Rui Shen: Zhejiang University of Technology
Ming Jiang: Zhejiang University of Technology

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 2, No 8, 377-387

Abstract: Abstract Penalty methods are very efficient in finding an optimal solution to constrained optimization problems. In this paper, we present an objective penalty function with two penalty parameters for inequality constrained bilevel programming under the convexity assumption to the lower level problem. Under some conditions, an optimal solution to a bilevel programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the objective penalty function, an algorithm is developed to obtain an optimal solution to the original bilevel programming, with its convergence proved under some conditions.

Keywords: Bilevel programming; Objective penalty function; Penalty function; Algorithm (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9945-9

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