A penalty method with trust-region mechanism for nonlinear bilevel optimization problem

We present a penalty method with trust-region technique for nonlinear bilevel optimization problem in this paper. This method follows Dennis, El-Alem, and Williamson active set idea and penalty method to transform the nonlinear bilevel optimization problem to unconstrained optimization problem. This...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 340; pp. 360 - 374
Main Authors El-Sobky, B., Abo-Elnaga, Y.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2018
Subjects
Active-set strategy
Global convergence
Nonlinear bilevel optimization problem
Penalty method
Trust-region
Trust-region
Global convergence
90C30
65K05
62C20
Nonlinear bilevel optimization problem
Active-set strategy
90B50
Penalty method
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Summary:We present a penalty method with trust-region technique for nonlinear bilevel optimization problem in this paper. This method follows Dennis, El-Alem, and Williamson active set idea and penalty method to transform the nonlinear bilevel optimization problem to unconstrained optimization problem. This method maybe simpler than similar ideas and it does not need to compute a base of the null space. A trust-region technique is used to globalize the algorithm. Global convergence theorem is presented and applications to mathematical programs with equilibrium constraints are given.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.03.004