一个求解P0函数非线性互补问题的非内部连续化算法

基于黄正海等2001年提出的光滑函数,本文给出一个求解P0函数非线性互补问题的非内部连续化算法.所给算法拥有一些好的特性.在较弱的条件下,证明了所给算法或者是全局线性收敛,或者是全局和局部超线性收敛.给出了所给算法求解两个标准测试问题的数值试验结果.     

解含多个复杂分量函数无约束minimax问题的积极集光滑化算法

本文利用分段三次多项式方程构造了一种积极集策略的二次连续可微的光滑化max函数,给出积极集及稳定的光滑化max函数的计算方法.基于该光滑化max函数,结合Armijo线搜索,负梯度和牛顿方向及光滑化参数的更新策略,给出一种解含多个复杂分量函数无约束minimax问题的积极集光滑化算法.初步的数值实验表明了该算法的有效性.     

求解摩擦接触问题的一个非内点光滑化算法

给出了一个求解三维弹性有摩擦接触问题的新算法,即基于NCP函数的非内点光滑化算法．首先通过参变量变分原理和参数二次规划法,将三维弹性有摩擦接触问题的分析归结为线性互补问题的求解;然后利用NCP函数,将互补问题的求解转换为非光滑方程组的求解;再用凝聚函数对其进行光滑化,最后用NEWTON法解所得到的光滑非线性方程组．方法具有易于理解及实现方便等特点．通过线性互补问题的数值算例及接触问题实例证实了该算法的可靠性与有效性．     

求解非线性互补问题一个新的Jacobian光滑化方法

本文构造了非线性互补问题一个新的光滑逼近函数,分析了该函数的一些基本性质.利用这一新的光滑逼近函数建立了求解非线性互补问题的一个Jacobi光滑化方法,并证明了在适当的条件下这一算法是全局及局部超线性收敛的.数值结果表明该方法是有效的.     

求解无限维非线性互补问题的光滑化牛顿法

研究一类无限维非线性互补问题的光滑化牛顿法.借助于非线性互补函数,将无限维非线性互补问题转化为一个非光滑算子方程.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化牛顿法具有超线性收敛性.     

基于二次函数光滑化逼近的修正低阶罚函数

针对不等式约束优化问题, 给出了通过二次函数对低阶精确罚函数进行光滑化逼近的两种函数形式, 得到修正的光滑罚函数. 证明了在一定条件下, 当罚参数充分大, 修正的光滑罚问题的全局最优解是原优化问题的全局最优解. 给出的两个数值例子说明了所提出的光滑化方法的有效性.     

基于新光滑函数的P0映射非线性互补问题的光滑牛顿法(英文)

非线性互补问题(NCP)可以重新表述为一个非光滑方程组的解.通过引入一个新的光滑函数,将问题近似为参数化光滑方程组.基于这个光滑函数,我们提出了一个求解P₀映射和R₀映射非线性互补问题的光滑牛顿法.该算法每次迭代只求解一个线性方程和一次线搜索.在适当的条件下,证明了该方法是全局和局部二次收敛的.数值结果表明,该算法是有效的.     

基于二次多项式的积极集光滑化max函数及其在无约束minimax问题中的应用

本文基于分段二次多项式方程,构造了一种积极集策略的光滑化max函数.通过给出与光滑化max函数相关的分量函数指标集的直接计算方法,将分段二次多项式方程转化为一般二次多项式方程.利用二次多项式方程根的性质,给出了该光滑化max函数的稳定计算策略,证明了其具有一阶光滑性,其梯度函数具有局部Lipschitz连续性和强半光滑性.该光滑化max函数仅与函数值较大的分量函数相关,适用于含分量函数较多且复杂的max函数的问题.为了验证其效率,本文基于该函数构造了一种解含多个复杂分量函数的无约束minimax问题的光滑化算法,数值实验表明了该光滑化max函数的可行性及有效性.     

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.     

基于凝聚函数的互补问题的光滑化算法

对于不可微的"极大值"形式的函数,可以利用凝聚函数对其进行光滑逼近.借助这个技术,给出了求解线性互补问题的光滑方程组算法.首先是将互补问题转化为等价的非光滑方程组,再利用凝聚函数进行光滑逼近,从而转化为光滑方程组的求解问题.通过一些考题对这个算法进行了数值试验,结果显示了该算法的有效性和稳定性.     

Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems

The mixed complementarity problem can be reformulated as a nonsmooth equation by using the median operator. In this paper, we first study some useful properties of this reformulation and then derive the Chen-Harker-Kanzow-Smale smoothing function for the mixed complementarity problem. On the basis of this smoothing function, we present a smoothing Newton method for solving the mixed complementarity problem. Under suitable conditions, the method exhibits global and quadratic convergence properties. We also present a smoothing Broyden-like method based on the same smoothing function. Under appropriate conditions, the method converges globally and superlinearly.     

数据挖掘中聚类中心问题的光滑化和填充函数方法

本文提出了数据挖掘中求解聚类中心问题的一种新方法.这类问题属于非凸非光滑全局最优化问题.我们首先利用光滑化方法将非光滑聚类函数用光滑函数逼近,然后对光滑化问题利用填充函数搜索其全局最优点.对不同数据库的数值试验表明,本文提出的算法是可行和有效的.     

A Smoothing Objective Penalty Function Algorithm for Inequality Constrained Optimization Problems

In this article, a smoothing objective penalty function for inequality constrained optimization problems is presented. The article proves that this type of the smoothing objective penalty functions has good properties in helping to solve inequality constrained optimization problems. Moreover, based on the penalty function, an algorithm is presented to solve the inequality constrained optimization problems, with its convergence under some conditions proved. Two numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.     

Second-Order Smoothing Objective Penalty Function for Constrained Optimization Problems

In this article, a novel objective penalty function as well as its second-order smoothing is introduced for constrained optimization problems (COP). It is shown that an optimal solution to the second-order smoothing objective penalty optimization problem is an optimal solution to the original optimization problem under some mild conditions. Based on the second-order smoothing objective penalty function, an algorithm that has better convergence is introduced. Numerical examples illustrate that this algorithm is efficient in solving COP.     

求解一类特殊非光滑极大值函数方程的光滑保守DPRP共轭梯度法

对一类特殊极大值函数非光滑方程问题的方法进行了研究, 利用极大值函数和绝对值函数的光滑函数对提出的非光滑方程问题进行转化, 提出了一种光滑保守DPRP共轭梯度法. 在一般的条件下, 给出了光滑保守DPRP共轭梯度法的全局收敛性, 最后给出相关的数值实验表明方法的有效性.     

Varying-coefficient model for the occurrence rate function of recurrent events

This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences (ALIVE) cohort study.     

A spline smoothing homotopy method for nonconvex nonlinear programming

Homotopy methods are globally convergent under weak conditions and robust; however, the efficiency of a homotopy method is closely related with the construction of the homotopy map and the path tracing algorithm. Different homotopies may behave very different in performance even though they are all theoretically convergent. In this paper, a spline smoothing homotopy method for nonconvex nonlinear programming is developed using cubic spline to smooth the max function of the constraints of nonlinear programming. Some properties of spline smoothing function are discussed and the global convergence of spline smoothing homotopy under the weak normal cone condition is proven. The spline smoothing technique uses a smooth constraint instead of m constraints and acts also as an active set technique. So the spline smoothing homotopy method is more efficient than previous homotopy methods like combined homotopy interior point method, aggregate constraint homotopy method and other probability one homotopy methods. Numerical tests with the comparisons to some other methods show that the new method is very efficient for nonlinear programming with large number of complicated constraints.