Double penalty method for bilevel optimization problems

Yo Ishizuka; Eitaro Aiyoshi

doi:10.1007/BF02098173

Double penalty method for bilevel optimization problems

Yo Ishizuka, Eitaro Aiyoshi

Department of Applied Physics and Physico-Informatics

Research output: Contribution to journal › Article › peer-review

51 Citations (Scopus)

Abstract

A penalty function method approach for solving a constrained bilevel optimization problem is proposed. In the algorithm, both the upper level and the lower level problems are approximated by minimization problems of augmented objective functions. A convergence theorem is presented. The method is applicable to the non-singleton lower-level reaction set case. Constraint qualifications which imply the assumptions of the general convergence theorem are given.

Original language	English
Pages (from-to)	73-88
Number of pages	16
Journal	Annals of Operations Research
Volume	34
Issue number	1
DOIs	https://doi.org/10.1007/BF02098173
Publication status	Published - 1992 Dec 1

ASJC Scopus subject areas

Decision Sciences(all)
Management Science and Operations Research

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10.1007/BF02098173

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title = "Double penalty method for bilevel optimization problems",

abstract = "A penalty function method approach for solving a constrained bilevel optimization problem is proposed. In the algorithm, both the upper level and the lower level problems are approximated by minimization problems of augmented objective functions. A convergence theorem is presented. The method is applicable to the non-singleton lower-level reaction set case. Constraint qualifications which imply the assumptions of the general convergence theorem are given.",

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AB - A penalty function method approach for solving a constrained bilevel optimization problem is proposed. In the algorithm, both the upper level and the lower level problems are approximated by minimization problems of augmented objective functions. A convergence theorem is presented. The method is applicable to the non-singleton lower-level reaction set case. Constraint qualifications which imply the assumptions of the general convergence theorem are given.

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