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数学与物理
应用数学进展
Vol. 4 No. 3 (August 2015)
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二阶锥规划的光滑非精确牛顿法
Smoothing Inexact Newton Method for the Second Order Cone Programming
DOI:
10.12677/AAM.2015.43033
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作者:
董丽
,
杨金根
:信阳师范学院数学与信息科学学院,河南 信阳 ;
徐思齐
:信阳师范学院土木工程学院,河南 信阳
关键词:
二阶锥规划
;
光滑非精确牛顿法
;
收敛性
;
Second-Order Cone Programming
;
Smoothing Inexact Newton Method
;
Convergence
摘要:
本文给出了一个新的求解二阶锥规划的光滑非精确牛顿法。在每次迭代时,新方法采用非精确牛顿法去求解一个方程组的解,降低了光滑牛顿法的计算量。在较弱条件下,证明了算法具有全局和局部二阶收敛性质。数值试验表明算法是有效的。
Abstract:
A new smoothing inexact Newton method is presented for solving the second-order cone pro-gramming. At each iteration, the method uses an inexact Newton method to solve the system of equations, which saves computation work of smoothing Newton methods. Under weak assumptions, our method is proved to have global and local quadratic convergence. Numerical experiments indicate that the proposed method is quite effective.
文章引用:
董丽, 徐思齐, 杨金根. 二阶锥规划的光滑非精确牛顿法[J]. 应用数学进展, 2015, 4(3): 271-276.
http://dx.doi.org/10.12677/AAM.2015.43033
参考文献
[
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]
Alizadeh, F. and Goldfarb, D. (2003) Second-order cone optimization. Mathematical Programming, 95, 3-51.
http://dx.doi.org/10.1007/s10107-002-0339-5
[
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]
Chi, X.N. and Liu, S.Y. (2009) A non-interior continuation method for second-order cone optimization. Optimization, 58, 965-979.
http://dx.doi.org/10.1080/02331930701763421
[
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Chi, X.N. and Liu, S.Y. (2009) A one-step smoothing Newton method for second-order cone programming. Journal of Computational and Applied Mathematics, 223, 114-123.
http://dx.doi.org/10.1016/j.cam.2007.12.023
[
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Fang, L., He, G.P. and Hu, Y.H. (2009) A new smoothing Newton-type method for second-order cone programming problems. Applied Mathematics and Computation, 215, 1020-1029.
http://dx.doi.org/10.1016/j.amc.2009.06.029
[
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Tang, J.Y., He, G.P., Dong, L. and Fang, L. (2011) A smoothing Newton method for second-order cone optimizationbased on a new smoothing function. Applied Mathe-matics and Computation, 218, 1317-1329.
http://dx.doi.org/10.1016/j.amc.2011.06.015
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汤京永, 贺国平 (2012) 一个新的求解二阶锥规划的非内部连续化算法. 应用数学, 1, 26-31.
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Fukushima, M., Luo, Z.Q. and Tseng, P. (2002) Smoothing functions for second-order-cone complementarity problems. SIAM Journal on Optimization, 12, 436-460.
http://dx.doi.org/10.1137/S1052623400380365
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