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A self-adaptive trust region method for the extended linear complementarity problems
Applications of Mathematics, Tome 54 (2009) no. 1, pp. 53-65
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By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under strict complementarity conditions.
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under strict complementarity conditions.
DOI : 10.1007/s10492-009-0004-x
Classification : 65K05, 65K10, 90C30, 90C33, 90C51
Keywords: extended linear complementarity; self-adaptive trust region method; global convergence; local superlinear convergence; trust region algorithm 
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     title = {A self-adaptive trust region method for the extended linear complementarity problems},
     journal = {Applications of Mathematics},
     pages = {53--65},
     year = {2009},
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Yu, Zhensheng; Li, Qiang. A self-adaptive trust region method for the extended linear complementarity problems. Applications of Mathematics, Tome 54 (2009) no. 1, pp. 53-65. doi: 10.1007/s10492-009-0004-x

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