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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

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 from an arbitrary...

A new non-interior continuation method for P 0 -NCP based on a SSPM-function

Liang Fang (2011)

Applications of Mathematics

In this paper, we consider a new non-interior continuation method for the solution of nonlinear complementarity problem with P 0 -function ( P 0 -NCP). The proposed algorithm is based on a smoothing symmetric perturbed minimum function (SSPM-function), and one only needs to solve one system of linear equations and to perform only one Armijo-type line search at each iteration. The method is proved to possess global and local convergence under weaker conditions. Preliminary numerical results indicate that...

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

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

Applications of Mathematics

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 in the sets...

A new simultaneous subgradient projection algorithm for solving a multiple-sets split feasibility problem

Yazheng Dang, Yan Gao (2014)

Applications of Mathematics

In this paper, we present a simultaneous subgradient algorithm for solving the multiple-sets split feasibility problem. The algorithm employs two extrapolated factors in each iteration, which not only improves feasibility by eliminating the need to compute the Lipschitz constant, but also enhances flexibility due to applying variable step size. The convergence of the algorithm is proved under suitable conditions. Numerical results illustrate that the new algorithm has better convergence than the...

A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization

Y. Q. Bai, F. Y. Wang, X. W. Luo (2010)

RAIRO - Operations Research

In this paper we propose a primal-dual interior-point algorithm for convex quadratic semidefinite optimization problem. The search direction of algorithm is defined in terms of a matrix function and the iteration is generated by full-Newton step. Furthermore, we derive the iteration bound for the algorithm with small-update method, namely, O( n log n ε ), which is best-known bound so far.

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