Displaying similar documents to “A new non-interior continuation method for P 0 -NCP based on a SSPM-function”

A smoothing Newton method for the second-order cone complementarity problem

Jingyong Tang, Guoping He, Li Dong, Liang Fang, Jinchuan Zhou (2013)

Applications of Mathematics

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In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP....

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...

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...

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...

A globally convergent non-interior point algorithm with full Newton step for second-order cone programming

Liang Fang, Guoping He, Li Sun (2009)

Applications of Mathematics

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A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start...