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Xiangsong Zhang Sanyang Liu Zhenhua Liu 《Journal of Computational and Applied Mathematics》2010,234(3):713-721
In this paper, we focus on the variational inequality problem. Based on the Fischer-Burmeister function with smoothing parameters, the variational inequality problem can be reformulated as a system of parameterized smooth equations, a non-interior-point smoothing method is presented for solving the problem. The proposed algorithm not only has no restriction on the initial point, but also has global convergence and local quadratic convergence, moreover, the local quadratic convergence is established without a strict complementarity condition. Preliminary numerical results show that the algorithm is promising. 相似文献
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Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P
0-Functions 总被引:1,自引:0,他引:1
By using the Fischer–Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth
equations and using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing trust
region algorithm for solving the NCP with P
0 functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under
a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict
complementarity condition.
This work was partially supported by the Research Grant Council of Hong Kong and the National Natural Science Foundation of
China (Grant 10171030). 相似文献
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The mixed complementarity problem (denote by MCP(F)) can be reformulated as the solution of a smooth system of equations. In the paper, based on a perturbed mid function, we propose a new smoothing function, which has an important property, not satisfied by many other smoothing function. The existence and continuity of a smooth path for solving the mixed complementarity problem with a P0 function are discussed. Then we presented a one-step smoothing Newton algorithm to solve the MCP with a P0 function. The global convergence of the proposed algorithm is verified under mild conditions. And by using the smooth and semismooth technique, the rate of convergence of the method is proved under some suitable assumptions. 相似文献
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半无限规划的一阶最优性条件和牛顿型算法 总被引:1,自引:1,他引:0
在Fischer-Burmeister非线性互补函数的基础上,得到了半无限规划问题的一个新的一阶必要条件,并将半无限规划问题转化成一个光滑的无约束优化问题,给出了适合该问题的一个Damp-Newton算法,数值例子表明:算法结构简单,数值计算有效. 相似文献
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针对约束非线性l_1问题不可微的特点,提出了一种光滑近似算法.该方法利用" "函数的光滑近似函数和罚函数技术将非线性l_1问题转化为无约束可微问题,并在适当的假设下,该算法是全局收敛的.初步的数值试验表明算法的有效性. 相似文献
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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
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本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率. 相似文献