垂直线性互补问题的一步全局线性和局部二次收敛光滑Newton法

基于凝聚函数,提出一个求解垂直线性互补问题的光滑Newton法.该算法具有以下优点:(i)每次迭代仅需解一个线性系统和实施一次线性搜索;(ⅱ)算法对垂直分块P0矩阵的线性互补问题有定义且迭代序列的每个聚点都是它的解.而且,对垂直分块P₀+R₀矩阵的线性互补问题,算法产生的迭代序列有界且其任一聚点都是它的解;(ⅲ)在无严格互补条件下证得算法即具有全局线性收敛性又具有局部二次收敛性.许多已存在的求解此问题的光滑Newton法都不具有性质(ⅲ).     

非线性互补问题的一种不可行非内点连续方法

基于 Chen- Mangasarian光滑函数的一个子类 ,针对单调非线性互补问题给出了一种不可行非内点连续方法预估校正算法 ,并在适当的条件下 ,证明了算法具有全局线性收敛性和局部二次收敛性。     

垂直线性互补问题的一种光滑算法

文中给出了垂直线性互补问题的一个新的光滑价值函数,不同于光滑化方法中的价值函数,它不包含任何必须趋向零的参数,因此算法中不涉及参数调整步骤,而且具有良好的强制性.基此价值函数,提出了求解垂直线性互补问题的一种阻尼Newton类算法,并证明了该算法对竖块P0+R0矩阵的垂直线性互补问题具有全局收敛性;当解满足相当于BD-正则条件时,算法具有局部二次收敛性;在不增加额外校正步骤(算法的每个迭代步只求解一个Newton方程)的情形下,算法对竖块P-矩阵垂直线性互补问题(无须假设严格互补),具有有限步收敛性.数值实验结果令人满意.     

非线性互补问题的一种不可行非内点连续算法

基于Chen-Harker—Kanzow-Smale光滑函数，对单调非线性互补问题NCP(f)给出了一种不可行非内点连续算法，该算法在每次迭代时只需求解一个线性等式系统，执行一次线搜索，算法在NCP(f)的解处不需要严格互补的条件下，具有全局线性收敛性和局部二次收敛性．     

处理退化问题的一类SQP算法

本文对不等式优化问题提出了一个修正的序列二次规划算法(SQP).该算法适用于退化问题一积极约束梯度线性相关且严格互补条件不成立,并且算法是可行的,具有整体收敛与超线性收敛性.     

最优化两个拓广的SQP和SSLE算法模型及其超线性和二次收敛性

给出一般约束最优化的序列二次规划（SQP）和序列线性方程组（SSLE）算法两个拓广的模型,详细分析和论证两个模型的局部超线性收敛性及二次收敛性条件,其中并不需要严格互补条件,拓广的模型及其收敛速度结果具有更广泛的适用性,为SQP和SSLE算法收敛速度的研究提供了更为完善和便利的理论基础。     

基于一个新的NCP函数的光滑牛顿法求解非线性互补问题

本文研究了非线性互补的光滑化问题.利用一个新的光滑NCP函数将非线性互补问题转化为等价的光滑方程组,并在此基础上建立了求解P0-函数非线性互补问题的一个完全光滑化牛顿法,获得了算法的全局收敛性和局部二次收敛性的结果.并给出数值实验验证了理论分析的正确性.     

求解特定线性互补问题的牛顿KKT内点法

利用线性互补问题与二次规划之间的关系,推广了求解二次规划的KKT内点法,并用于线性互补问题,分析了推广算法的全局收敛性和局部收敛性.数值实验表明,算法对求解几类线性互补问题是有效的.     

有奇异解的无约束最优化问题的一种混合法

本文研究求解含有奇异解的无约束最优化问题算法 .该类问题的一个重要特性是目标函数的Hessian阵可能处处奇异 .我们提出求解该类问题的一种梯度 -正则化牛顿型混合算法 .并在一定的条件下得到了算法的全局收敛性 .而且 ,经一定迭代步后 ,算法还原为正则化 Newton法 .因而 ,算法具有局部二次收敛性 .     

P0函数非线性互补问题的一步非内点连续方法的收敛性

本文对于P0函数非线性互补问题提出了一个基于Kanzow光滑函数的一步非内点连续方法,在适当的假设条件下,证明了方法的全局线性及局部二次收敛性.特别,在方法的全局线性收敛性的分析中,不需要假定非线性互补问题的函数的Jacobi阵是Lipschitz连续的.文献中为了得到非内点连续方法的全局线性收敛性,这一假定是被广泛使用的.本文提出的方法在每一次迭代只须解一个线性方程式组.     

A non-interior-point smoothing method for variational inequality problem

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.     

A smoothing Levenberg–Marquardt method for the extended linear complementarity problem

We consider the extended linear complementarity problem (XLCP), of which the linear and horizontal linear complementarity problems are two special cases. We reformulate the XLCP to a smooth equation by using some smoothing functions and propose a Levenberg–Marquardt method to solve the system of smooth equation. The global convergence and local superlinear convergence rate are established under certain conditions. Numerical tests show the effectiveness of the proposed algorithm.     

A Non-Interior Continuation Algorithm for the P0 or P* LCP with Strong Global and Local Convergence Properties

We propose a non-interior continuation algorithm for the solution of the linear complementarity problem (LCP) with a P₀ matrix. The proposed algorithm differentiates itself from the current continuation algorithms by combining good global convergence properties with good local convergence properties under unified conditions. Specifically, it is shown that the proposed algorithm is globally convergent under an assumption which may be satisfied even if the solution set of the LCP is unbounded. Moreover, the algorithm is globally linearly and locally superlinearly convergent under a nonsingularity assumption. If the matrix in the LCP is a P_* matrix, then the above results can be strengthened to include global linear and local quadratic convergence under a strict complementary condition without the nonsingularity assumption.     

解P_0非线性互补问题的光滑Levenberg-Marquardt方法

本文研究了一个P0非线性互补问题.利用信赖域技术获得了求解该问题的光滑Levenberg-Marquardt算法,该算法在一定条件下具有全局性.利用局部误差界还获得了该算法的超线性和二次收敛.数值结果表明该算法是有效的.     

An algorithm for a class of nonlinear complementarity problems with non-Lipschitzian functions

In this paper, we focus on solving a class of nonlinear complementarity problems with non-Lipschitzian functions. We first introduce a generalized class of smoothing functions for the plus function. By combining it with Robinson's normal equation, we reformulate the complementarity problem as a family of parameterized smoothing equations. Then, a smoothing Newton method combined with a new nonmonotone line search scheme is employed to compute a solution of the smoothing equations. The global and local superlinear convergence of the proposed method is proved under mild assumptions. Preliminary numerical results obtained applying the proposed approach to nonlinear complementarity problems arising in free boundary problems are reported. They show that the smoothing function and the nonmonotone line search scheme proposed in this paper are effective.     

非线性互补问题的SQP方法

In this paper, the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints ,and a SQP algorithm for this reformulation based on a damped Gauss-Newton type method is presented. It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

求解非线性互补问题的一个下降算法(英文)

在[1]中,Solodov将非线性互补问题等价地转化成一个带非负约束的优化问题.基于这种转化形式,我们给出了一种求解非线性互补问题的下降算法.在映射为强单调时,证明了算法的全局收敛性.     

求解张量随机互补问题的光滑牛顿算法

近年来, 越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量, 并提出了张量随机互补问题。本文通过引入一类光滑函数, 提出了求解张量随机互补问题的一种光滑牛顿算法, 并证明了算法的全局和局部收敛性, 最后通过数值实验验证了算法的有效性。