共查询到20条相似文献,搜索用时 31 毫秒
1.
XiuNaihua 《高校应用数学学报(英文版)》2000,15(4):433-442
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. 相似文献
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We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs.This research was supported by the Singapore-MIT Alliance and the Australian Research Council. 相似文献
4.
A smoothing-type algorithm for solving system of inequalities 总被引:1,自引:0,他引:1
Zheng-Hai Huang Ying Zhang Wei Wu 《Journal of Computational and Applied Mathematics》2008,220(1-2):355-363
In this paper we consider system of inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A Newton-type algorithm is applied to solve iteratively the smooth equations so that a solution of the problem concerned is found. We show that the algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results are reported. 相似文献
5.
Changyu Wang Chengyun Gao Zhenjun Shi 《Computational Optimization and Applications》1997,7(2):239-253
In this paper, we extend the ordinary discrete type facility location problems to continuous type ones. Unlike the discrete type facility location problem in which the objective function isn't everywhere differentiable, the objective function in the continuous type facility location problem is strictly convex and continuously differentiable. An algorithm without line search for solving the continuous type facility location problems is proposed and its global convergence, linear convergence rate is proved. Numerical experiments illustrate that the algorithm suggested in this paper have smaller amount of computation, quicker convergence rate than the gradient method and conjugate direction method in some sense. 相似文献
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Chang-fengMa Pu-yanNie Guo-pingLiang 《计算数学(英文版)》2003,21(6):747-758
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. 相似文献
8.
Liping Zhang 《Operations Research Letters》2003,31(2):161-166
We study the spherical facility location problem which is a more realistic model than the Euclidean facilities location. We present a modified algorithm for this problem, which has the following good properties: (a) It is very easy to initialize the algorithm with an arbitrary point as its starting point; (b) Under suitable assumptions, it is proved that the algorithm globally converges to a global minimizer of the problem. 相似文献
9.
In this paper, a new sequential penalty algorithm, based on the Linfin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. 相似文献
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Geurt Jongbloed 《Journal of computational and graphical statistics》2013,22(3):310-321
Abstract The problem of minimizing a smooth convex function over a specific cone in IRn is frequently encountered in nonparametric statistics. For that type of problem we suggest an algorithm and show that this algorithm converges to the solution of the minimization problem. Moreover, a simulation study is presented, showing the superiority of our algorithm compared to the EM algorithm in the interval censoring case 2 setting. 相似文献
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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.
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
14.
A semismooth equation approach to the solution of nonlinear complementarity problems 总被引:20,自引:0,他引:20
In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on
a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to
semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously
differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild
assumptions. Other interesting features of the new algorithm are an extreme simplicity along with a low computational burden
per iteration. We include numerical tests which show the viability of the approach. 相似文献
15.
Tie Ni 《Applied mathematics and computation》2010,216(7):2207-3378
The smoothing-type algorithm has been successfully applied to solve various optimization problems. In general, the smoothing-type algorithm is designed based on some monotone line search. However, in order to achieve better numerical results, the non-monotone line search technique has been used in the numerical computations of some smoothing-type algorithms. In this paper, we propose a smoothing-type algorithm for solving the nonlinear complementarity problem with a non-monotone line search. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported. 相似文献
16.
Zheng-Hai Huang Defeng Sun Gongyun Zhao 《Computational Optimization and Applications》2006,35(2):199-237
In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject
to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger
local superlinear convergence. Preliminary numerical results are also reported.
Mathematics Subject Classification (1991): 90C33, 65K10
This author’s work was also partially supported by the Scientific Research Foundation of Tianjin University for the Returned
Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin
University. 相似文献
17.
Guoliang Xue 《Numerical Algorithms》1995,9(1):1-12
In this paper we partially resolve an open problem in spherical facility location. The spherical facility location problem is a generalization of the planar Euclidean facility location problem. This problem was first studied by Katz and Cooper and by Drezner and Wesolowsky where a Weszfeld-like algorithm was proposed. This algorithm is very simple and does not require a line search. However, its convergence has been an open problem for more than ten years. In this paper, we prove that the sequence generated by the algorithm converges to the unique optimal solution under the condition that the oscillation of the sequence converges to zero. We conjecture that the algorithm is a descent algorithm and prove that the sequence generated by the algorithm converges to the optimal solution under this conjecture. 相似文献
18.
提出一种改进的求解极小极大问题的信赖域滤子方法,利用SQP子问题来求一个试探步,尾服用滤子来衡量是否接受试探步,避免了罚函数的使用;并且借用已有文献的思想, 使用了Lagrange函数作为效益函数和非单调技术,在适当的条件下,分析了算法的全局和局部收敛性,并进行了数值实验. 相似文献
19.
Fenghui Wang 《Optimization》2017,66(3):407-415
The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we propose a new algorithm for this problem that is completely different from the existing algorithms. Moreover, our algorithm does not need any prior information of the operator norm. Under standard assumptions, we establish a weak convergence theorem of the proposed algorithm and a strong convergence theorem of its variant. 相似文献