共查询到10条相似文献,搜索用时 234 毫秒
1.
We propose a new smoothing Newton method for solving the P
0-matrix linear complementarity problem (P
0-LCP) based on CHKS smoothing function. Our algorithm solves only one linear system of equations and performs only one line search per iteration. It is shown to converge to a P
0-LCP solution globally linearly and locally quadratically without the strict complementarity assumption at the solution. To the best of author's knowledge, this is the first one-step smoothing Newton method to possess both global linear and local quadratic convergence. Preliminary numerical results indicate that the proposed algorithm is promising. 相似文献
2.
A new smoothing function for the second-order cone programming is given by smoothing the symmetric perturbed Fischer–Burmeister function. Based on this new function, a one-step smoothing Newton method is presented for solving the second-order cone programming. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. This algorithm does not have restrictions regarding its starting point and is Q-quadratically convergent. Numerical results suggest the effectiveness of our algorithm. 相似文献
3.
《Optimization》2012,61(8):965-979
We extend the smoothing function proposed by Huang, Han and Chen [Journal of Optimization Theory and Applications, 117 (2003), pp. 39–68] for the non-linear complementarity problems to the second-order cone programming (SOCP). Based on this smoothing function, a non-interior continuation method is presented for solving the SOCP. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that our algorithm is globally and locally superlinearly convergent in absence of strict complementarity at the optimal solution. Numerical results indicate the effectiveness of the algorithm. 相似文献
4.
Jingyong Tang Guoping HeLi Dong Liang Fang 《Applied mathematics and computation》2011,218(4):1317-1329
A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods. 相似文献
5.
6.
In this paper, we present a new one‐step smoothing Newton method for solving the second‐order cone complementarity problem (SOCCP). Based on a new smoothing function, the SOCCP is approximated by a family of parameterized smooth equations. At each iteration, the proposed algorithm only need to solve one system of linear equations and perform only one Armijo‐type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the SOCCP solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
7.
LiPingZHANG JiYeHAN ZhengHaiHUANG 《数学学报(英文版)》2005,21(1):117-128
We propose a one-step smoothing Newton method for solving the non-linear complementarity problem with P0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function(for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0-NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions. 相似文献
8.
Liu YangYanping Chen Xiaojiao TongChunlin Deng 《Applied mathematics and computation》2011,217(24):9855-9863
In this paper, a new smoothing Newton method is proposed for solving constrained nonlinear equations. We first transform the constrained nonlinear equations to a system of semismooth equations by using the so-called absolute value function of the slack variables, and then present a new smoothing Newton method for solving the semismooth equations by constructing a new smoothing approximation function. This new method is globally and quadratically convergent. It needs to solve only one system of unconstrained equations and to perform one line search at each iteration. Numerical results show that the new algorithm works quite well. 相似文献
9.
圆锥规划是一类重要的非对称锥优化问题.基于一个光滑函数,将圆锥规划的最优性条件转化成一个非线性方程组,然后给出求解圆锥规划的光滑牛顿法.该算法只需求解一个线性方程组和进行一次线搜索.运用欧几里得约当代数理论,证明该算法具有全局和局部二阶收敛性.最后数值结果表明算法的有效性. 相似文献