A predictor-corrector smoothing method for second-order cone programming

被引：0

作者：

Zhang X. ^{[1
]}

Liu S. ^{[1
]}

Liu Z. ^{[1
]}

机构：

[1] Applied Mathematics Department, Xidian University, Xi'an

来源：

Journal of Applied Mathematics and Computing | 2010年 / 32卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Local quadratic convergence; Predictor-corrector smoothing Newton method; Second-order cone programming;

D O I：

10.1007/s12190-009-0256-3

中图分类号：

学科分类号：

摘要：

In this paper, the second order cone programming problem is studied. By introducing a parameter into the Fischer-Burmeister function, a predictor-corrector smoothing Newton method for solving the problem is presented. The proposed algorithm does neither have restrictions on its starting point nor need additional computation which keep the iteration sequence staying in the given neighborhood. Furthermore, the global and the local quadratic convergence of the algorithm are obtained, among others, the local quadratic convergence of the algorithm is established without strict complementarity. Preliminary numerical results indicate that the algorithm is effective. © 2009 Korean Society for Computational and Applied Mathematics.

引用

页码：369 / 381

页数：12

共 21 条

[1]

Alizadeh F., Goldfarb D., Second-order cone programming, Mathematical Programming, Series B, 95, 1, pp. 3-51, (2003)

[2]

Burke J., Xu S., A noninterior predictor-corrector path-following algorithm for the monotone linear complementarily problem, Math. Program, 87, pp. 113-130, (2000)

[3]

Clark F.H., Optimization and Nonsmooth Analysis, (1993)

[4]

Chen X.D., Sun D., Sun J., Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems, Comput. Optim. Appl., 25, pp. 39-56, (2003)

[5]

Chi X., Liu S., Analysis of a non-interior continuation method for second order cone programming, J. Appl. Math. Comput., 27, pp. 47-61, (2008)

[6]

Chen X., Tseng P., Non-interior continuation methods for solving semidefinite complementarity problems, Mathematical Programming, Series B, 95, 3, pp. 431-474, (2003)

[7]

Chen B., Xiu N., A global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions, SIAM J. Optim., 9, pp. 605-623, (1999)

[8]

Faraut J., Koranyi A., Analysis on Symmetric Cones, (1994)

[9]

Fukushima M., Luo Z.Q., Tseng P., Smoothing functions for second-order cone complementarity problems, SIAM J. Optim., 12, pp. 436-460, (2001)

[10]

Gowda M.S., Sznajder R., Tao J., Some P-properties for linear transformations on Euclidean Jordan algebras, Linear Algebra Appl., 393, pp. 203-232, (2004)

← 1 2 3 →