A trust region algorithm for solving bilevel programming problems |
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| Authors: | Guo-shan Liu Shi-qin Xu Ji-ye Han |
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| Institution: | [1]School of Business, Renmin University of China, Beijing 100872, China [2]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| 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. |
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| Keywords: | Bilevel programming problem trust region algorithm global convergence mathematical program with equilibrium constraints stationary point |
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