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A trust region algorithm for solving bilevel programming problems

A trust region algorithm for solving bilevel programming problems In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A trust region algorithm for solving bilevel programming problems

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-013-0231-5
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 20, 2013

References