共查询到18条相似文献,搜索用时 140 毫秒
1.
《数学的实践与认识》2013,(17)
提出了一组无界性条件,在此基础上给出了求解一类无界非凸非线性规划问题的K-K-T点的一种高效的全局收敛性算法,在适当的条件下,给出了算法的收敛性证明.结果把已有的研究结果推广到无界区域上,进一步扩大了算法的求解区域. 相似文献
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给出了求解无界非凸规划的K-K-T系统的一种连续化方法,在适当的条件下,得到了连接可行域内部任意给定的点和非凸规划的K-K-T点的同伦路径存在性的构造性证明,从而构建了可数值实现的全局收敛性算法.数值算例进一步验证了本文结果的有效性. 相似文献
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组合同伦方法在无界域上的收敛性 总被引:3,自引:0,他引:3
组合同伦内点法由Feng等提出,是求解有界区域上的非凸数学规划的一种大范围收敛性方法,本文证明此算法适用于某些无界区域上的非凸数学规划问题。 相似文献
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Hager和Zhang[4]提出了一种新的非线性共轭梯度法(简称 HZ 方法), 并证明了该方法在 Wolfe搜索和 Goldstein 搜索下求解强凸问题的全局收敛性.但是HZ方法在标准Armijo 搜索下求解非凸问题是否全局收敛尚不清楚.该文提出了一种保守的HZ共轭梯度法,并且证明了这种方法在 Armijo 线性搜索下求解非凸优化问题的全局收敛性.此外,作者给出了一些 数值结果以检验该方法的有效性. 相似文献
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同伦方法求解非凸区域Brouwer不动点问题 总被引:2,自引:0,他引:2
本文构造了一个新的求解非凸区域上不动点问题的内点同伦算法,并在弱法锥(见定义2.1(2))和适当的条件下,证明了算法的全局收敛性.本文所给的条件比外法锥条件更加一般. 相似文献
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利用同伦方法求解非凸规划时,一般只能得到问题的K-K-T点.本文得到无界域上同伦方法求解非凸规划的几个收敛性定理,证明在一定条件下,通过构造合适的同伦方程,同伦算法收敛到问题的局部最优解. 相似文献
7.
《高校应用数学学报(A辑)》2021,36(2)
提出了一种非内点同伦方法来解决无界集上的双层规划问题,并在适当的假设条件下,证明了同伦路径的存在性和全局收敛性.这种方法放宽了对初始点的要求,使数值计算更加便利.数值结果表明,该方法与现有的解双层规划问题的同伦方法相比,计算效率更高. 相似文献
8.
本文给出了一个修改的路径跟踪预测校正非内点算法 ,同时给出了一个新的中心路邻域的表示 .并在此基础上给出了全局和局部收敛性 ,最后给出的数值结果验证了其有效性 相似文献
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As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets. 相似文献
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In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm. 相似文献
13.
In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of Rn, which may improve greatly the computational efficiency of reduced predictor-corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper. 相似文献
14.
In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper. 相似文献
15.
Muhammad Aslam Noor 《Applicable analysis》2013,92(5):777-786
In this article, we introduce and consider a new system of general nonconvex variational inequalities involving four different operators. We use the projection operator technique to establish the equivalence between the system of general nonconvex variational inequalities and the fixed points problem. This alternative equivalent formulation is used to suggest and analyse some new explicit iterative methods for this system of nonconvex variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of nonconvex variational inequalities, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results can be viewed as a refinement and an improvement of the previously known results for variational inequalities. 相似文献
16.
Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting. 相似文献
17.
《Optimization》2012,61(6):845-854
Through a suitable application of Toland's duality theory to certain nonconvex and nonsmooth problems one obtain an unbounded minimization problem with Fréchet:-differentiable cost function as dual problem and one can establish a gradient projection method for the solution of these problems. 相似文献
18.
The purpose of this paper is to introduce and study split systems of general nonconvex variational inequalities. Taking advantage of the projection technique over uniformly prox-regularity sets and utilizing two nonlinear operators, we propose and analyze an iterative scheme for solving the split systems of general nonconvex variational inequalities and fixed point problems. We prove that the sequence generated by the suggested iterative algorithm converges strongly to a common solution of the foregoing split problem and fixed point problem. The result presented in this paper extends and improves some well-known results in the literature. Numerical example illustrates the theoretical result. 相似文献