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1.
提出一类新的求解无约束优化问题的记忆梯度法,证明了算法的全局收敛性.当目标函数为一致凸函数时,对其线性收敛速率进行了分析.新算法在迭代过程中无需对步长进行线性搜索,仅需对算法中的一些参数进行预测估计,从而减少了目标函数及梯度的迭代次数,降低了算法的计算量和存储量.数值试验表明算法是有效的.  相似文献   

2.
在利用Fischer-Burmeister函数将非线性互补问题转化为非线性方程组的基础上,本文通过将信赖域方法与线性搜索方法结合起来,提出了求解一般非线性互补问题的光滑化方法.算法中我们给出了一个特定条件,条件满足时,采用信赖步,条件不满足时.采用梯度步.我们证明了算法具有全局收敛性.在解是R-正则的条件下,收敛速度是Q-超线性/Q-二阶收敛的.  相似文献   

3.
一类新的曲线搜索下的多步下降算法   总被引:1,自引:0,他引:1  
提出一类新的曲线搜索下的多步下降算法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率.算法利用前面多步迭代点的信息和曲线搜索技巧产生新的迭代点,收敛稳定,不用计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.  相似文献   

4.
基于光滑Fischer-Burmeister函数,本文给出一个新的求解二阶锥规划的非内部连续化算法.算法对初始点的选取没有任何限制,并且在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补条件下,证明了算法是全局收敛且是局部超线性收敛的.数值试验表明算法是有效的.  相似文献   

5.
袁敏  万中 《计算数学》2014,36(1):35-50
提出了一种新的磨光函数,在分析它与已有磨光函数不同特性的基础上,研究了将它用于求解非线性P_0互补问题时,其磨光路径的存在性和连续性,进而设计了求解一类非线性P_0互补问题的非单调磨光算法.在适当的假设条件下,证明了该算法的全局收敛性和局部超线性收敛性.数值算例验证了算法的有效性.  相似文献   

6.
董丽  王洪芹  潘虹 《数学杂志》2015,35(6):1453-1460
本文研究了二阶锥规划问题.利用新的最小值函数的光滑函数,给出一个求解二阶锥规划的光滑牛顿算法.算法可以从任意点出发,在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补假设条件下,证明了算法是全局收敛和局部二阶收敛的.数值试验表明算法是有效的.  相似文献   

7.
借助于半罚函数和产生工作集的识别函数以及模松弛SQP算法思想,建立了求解带等式及不等式约束优化的一个新算法.每次迭代中,算法的搜索方向由一个简化的二次规划子问题及一个简化的线性方程组产生.算法在不包含严格互补性的温和条件下具有全局收敛性和超线性收敛性.最后给出了算法初步的数值试验报告.  相似文献   

8.
高岳林  井霞 《计算数学》2013,35(1):89-98
提出了求解一类线性乘积规划问题的分支定界缩减方法, 并证明了算法的收敛性.在这个方法中, 利用两个变量乘积的凸包络技术, 给出了目标函数与约束函数中乘积的下界, 由此确定原问题的一个松弛凸规划, 从而找到原问题全局最优值的下界和可行解. 为了加快所提算法的收敛速度, 使用了超矩形的缩减策略. 数值结果表明所提出的算法是可行的.  相似文献   

9.
基于一个有效约束识别技术, 给出了具有不等式约束的非线性最优化问题的一个可行SSLE算法. 为获得搜索方向算法的每步迭代只需解两个或三个具有相同系数矩阵的线性方程组. 在一定的条件下, 算法全局收敛到问题的一个KKT点. 没有严格互补条件, 在比强二阶充分条件弱的条件下算法具有超线性收敛速度.  相似文献   

10.
本文针对不等式约束优化问题,结合Facchinei-Fischer-Kanzow精确有效集识别技术,给出—个新的线性方程组与辅助方向相结合的可行下降算法.算法每步迭代只需求解一个降维的线性方程组或计算一次辅助方向,且获取辅助方向的投影矩阵只涉及近似有效约束集中的元素,问题规模大为减少,且当迭代次数充分大时,只需求解一个降维的线性方程组.无需严格互补松弛条件,算法全局且一步超线性收敛.  相似文献   

11.
《Optimization》2012,61(8):965-979
We extend the smoothing function proposed by Huang, Han and Chen [Journal of Optimization Theory and Applications, 117 (2003), pp. 39–68] for the non-linear complementarity problems to the second-order cone programming (SOCP). Based on this smoothing function, a non-interior continuation method is presented for solving the SOCP. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that our algorithm is globally and locally superlinearly convergent in absence of strict complementarity at the optimal solution. Numerical results indicate the effectiveness of the algorithm.  相似文献   

12.
Convergence of a non-interior continuation algorithm for the monotone SCCP   总被引:1,自引:0,他引:1  
It is well known that the symmetric cone complementarity problem(SCCP) is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.  相似文献   

13.
The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex (or even uniformly convex). We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.  相似文献   

14.
This paper is devoted to globally convergent methods for solving large sparse systems of nonlinear equations with an inexact approximation of the Jacobian matrix. These methods include difference versions of the Newton method and various quasi-Newton methods. We propose a class of trust region methods together with a proof of their global convergence and describe an implementable globally convergent algorithm which can be used as a realization of these methods. Considerable attention is concentrated on the application of conjugate gradient-type iterative methods to the solution of linear subproblems. We prove that both the GMRES and the smoothed COS well-preconditioned methods can be used for the construction of globally convergent trust region methods. The efficiency of our algorithm is demonstrated computationally by using a large collection of sparse test problems.  相似文献   

15.
In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010) and Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)  相似文献   

16.
本文将利用梯度投影与Fisher函数提出一个新的二阶段搜索方向,给出相应的解非线性不等式约束优化问题的梯度投影算法,并证明了该算法具有全局收敛性.  相似文献   

17.
1. IntroductionConsider the optimization problemmin {f(x): gi(x) 5 0, j E I; x E R"}, (l)where f(x), gi(x): Rad - R, j E I ~ {1, 2,...,m}.It is well known that one of the most effective methods to solve problem (1) is thesequential quadratic programming (i.e., SoP) (see [1--6]), due to its property of superlinearconvergence. Especially in recent years, in order to perfect SoP both in theory and application, there have many papers, such as [7--10], been published. These papers focus mainly…  相似文献   

18.
A function mapping from n to is called an SC1-function if it is differentiable and its derivative is semismooth. A convex SC1-minimization problem is a convex minimization problem with an SC1-objective function and linear constraints. Applications of such minimization problems include stochastic quadratic programming and minimax problems. In this paper, we present a globally and superlinearly convergent trust-region algorithm for solving such a problem. Numerical examples are given on the application of this algorithm to stochastic quadratic programs.This work was supported by the Australian Research Council.We are indebted to Dr. Xiaojun Chen for help in the computation. We are grateful to two anonymous referees for their comments and suggestions, which improved the presentation of this paper.  相似文献   

19.
Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.  相似文献   

20.
The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.  相似文献   

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