Displaying similar documents to “Augmented Lagrangian methods for variational inequality problems”

A self-adaptive trust region method for the extended linear complementarity problems

Zhensheng Yu, Qiang Li (2009)

Applications of Mathematics

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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...

A new one-step smoothing newton method for second-order cone programming

Jingyong Tang, Guoping He, Li Dong, Liang Fang (2012)

Applications of Mathematics

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In this paper, we present a new one-step smoothing Newton method for solving the second-order cone programming (SOCP). Based on a new smoothing function of the well-known Fischer-Burmeister function, the SOCP is approximated by a family of parameterized smooth equations. Our algorithm solves only one system of linear equations and performs only one Armijo-type line search at each iteration. It can start from an arbitrary initial point and does not require the iterative points to be...

Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

Jingyong Tang, Li Dong, Liang Fang, Li Sun (2015)

Applications of Mathematics

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The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which...