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带NCP函数的信赖域滤子方法 总被引:2,自引:0,他引:2
滤子方法最初是由Fletcher和Leyffer在2002年提出的.这种方法的原理是:在一个试探步,如果相应的目标函数值或约束违反度函数值下降,那么该试探步就会被接受.利用Fischer-Burmeister NCP函数来修正滤子中的约束违反度函数,同时证明了这个新的滤子方法具有全局收敛性. 相似文献
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本文给出新的NCP函数,这些函数是分段线性有理正则伪光滑的,且具有良好的性质.把这些NCP函数应用到解非线性优化问题的方法中.例如,把求解非线性约束优化问题的KKT点问题分别用QP-free方法,乘子法转化为解半光滑方程组或无约束优化问题.然后再考虑用非精确牛顿法或者拟牛顿法来解决该半光滑方程组或无约束优化问题.这个方法是可实现的,且具有全局收敛性.可以证明在一定假设条件下,该算法具有局部超线性收敛性. 相似文献
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在经营管理、工程设计、科学研究、军事指挥等方面普遍存在着最优化问题,而实际问题中出现的绝大多数问题都被归纳为非线性规划问题之中。作为带等式、不等式约束的复杂事例,最优化问题的求解向来较为繁琐、困难。适当条件下,非线性互补函数(NCP)可以与约束优化问题相结合,其中NCP函数的无约束极小解对应原约束问题的解及其乘子。本文提出了一类新的NCP函数用于解决等式和不等式约束非线性规划问题,结合新的NCP函数构造了增广Lagrangian函数。在适当假设条件下,证明了增广Lagrangian函数与原问题的解之间的一一对应关系。同时构造了相应算法,并证明了该算法的收敛性和有效性。 相似文献
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本文针对非线性规划给出了一种修改的带NCP函数的信赖域滤子SQP算法,主要的修改之处是用NCP函数替代了滤子中约束违反度函数,而且进一步证明了这种修改的算法同样具有全局收敛性. 相似文献
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线性正则变换是经典Fourier变换的广义形式,目前在非平稳信号的参数检测与估计方面取得了优异的应用效果,但线性正则变换理论体系还不完善.探讨了线性正则变换相关的复能量密度函数的基本概念,并详细推导研究了其基本的数学性质与特点,在上述理论的基础上,通过仿真实验来验证所得到结论的准确性.为其在实际应用中发挥更大的作用奠定了基础. 相似文献
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PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD 总被引:3,自引:0,他引:3
Pu Dingguo Zhou Yan 《高校应用数学学报(英文版)》2006,21(3):289-301
In this paper,a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems.The new NCP functions are piece- wise linear-rational,regular pseudo-smooth and have nice properties.This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions,by using the piecewise NCP functions.This method is implementable and globally convergent without assuming the strict complementarity condition,the isolatedness of accumulation points.Fur- thermore,the gradients of active constraints are not requested to be linearly independent.The submatrix which may be obtained by quasi-Newton methods,is not requested to be uniformly positive definite.Preliminary numerical results indicate that this new QP-free method is quite promising. 相似文献
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We consider a class of stochastic linear complementarity problems (SLCPs) with finitely many realizations. In this paper we
reformulate this class of SLCPs as a constrained minimization (CM) problem. Then, we present a feasible semismooth Newton
method to solve this CM problem. Preliminary numerical results show that this CM reformulation may yield a solution with high
safety for SLCPs. 相似文献
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We consider the problem of minimizing an SC1 function subject to inequality constraints. We propose a local algorithm whose distinguishing features are that: (a) a fast convergence rate is achieved under reasonable assumptions that do not include strict complementarity at the solution; (b) the solution of only linear systems is required at each iteration; (c) all the points generated are feasible. After analyzing a basic Newton algorithm, we propose some variants aimed at reducing the computational costs and, in particular, we consider a quasi-Newton version of the algorithm. 相似文献
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本文利用一个新的分片线性NCP函数提出一个新的可行的QP-free方法解非线性不等式约束优化问题.不同于其他的QP-free方法,这个方法只考虑在工作集中的约束函数,工作集是积极集的一个估计,因此子问题的维数不是满秩的.这个方法可行的并且不需假定严格互补条件、聚点的孤立性得到算法的全局收敛性,并且积极约束函数的梯度不要求线性独立的,其中由拟牛顿法得到的子矩阵不需要求一致正定性. 相似文献
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Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization 总被引:2,自引:0,他引:2
A new, infeasible QP-free algorithm for nonlinear constrained optimization problems is proposed. The algorithm is based on a continuously differentiable exact penalty function and on active-set strategy. After a finite number of iterations, the algorithm requires only the solution of two linear systems at each iteration. We prove that the algorithm is globally convergent toward the KKT points and that, if the second-order sufficiency condition and the strict complementarity condition hold, then the rate of convergence is superlinear or even quadratic. Moreover, we incorporate two automatic adjustment rules for the choice of the penalty parameter and make use of an approximated direction as derivative of the merit function so that only first-order derivatives of the objective and constraint functions are used. 相似文献
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提出一种新的序列线性方程组(SSLE)算法解非线性不等式约束优化问题.在算法的每步迭代,子问题只需解四个简化的有相同的系数矩阵的线性方程组.证明算法是可行的,并且不需假定聚点的孤立性、严格互补条件和积极约束函数的梯度的线性独立性得到算法的全局收敛性.在一定条件下,证明算法的超线性收敛率. 相似文献