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排序方式: 共有107条查询结果,搜索用时 656 毫秒
1.
Satoru Ibaraki Masao Fukushima Toshihide Ibaraki 《Computational Optimization and Applications》1992,1(2):207-226
A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs. 相似文献
2.
框式约束凸二次规划问题的内点算法 总被引:4,自引:0,他引:4
张艺 《高等学校计算数学学报》2002,24(2):163-168
In this paper,a primal-dual interior point algorithm for convex quadratic progromming problem with box constrains is presented.It can be started at any primal-dual interior feasible point.If the initial point is close to the central path,it becomes a central path-following alogorithm and requires a total of O(√nL)number of iterations,where L is the input length. 相似文献
3.
Y. Zhang 《Journal of Optimization Theory and Applications》1993,77(2):323-341
This paper concerns solving an overdetermined linear systemA
T
x=b in the leastl
1-norm orl
-norm sense, whereA
m×n
,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel
1 andl
-problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA
T
, whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100. 相似文献
4.
We present an algorithm for variational inequalities VI(
, Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping
is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one. 相似文献
5.
Gianni Di Pillo Stefano Lucidi Laura Palagi 《Computational Optimization and Applications》1999,12(1-3):157-188
In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs
converging quadratically to a pair
where
satisfies the first order necessary conditions and
is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence x
k alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported. 相似文献
6.
Tsung-Min Hwang Chih-Hung Lin Wen-Wei Lin Shu-Cherng Fang 《Annals of Operations Research》1996,62(1):173-196
In this paper, we provide an easily satisfied relaxation condition for the primaldual interior path-following algorithm to solve linear programming problems. It is shown that the relaxed algorithm preserves the property of polynomial-time convergence. The computational results obtained by implementing two versions of the relaxed algorithm with slight modifications clearly demonstrate the potential in reducing computational efforts.Partially supported by the North Carolina Supercomputing Center, the 1993 Cray Research Award, and a National Science Council Research Grant of the Republic of China. 相似文献
7.
Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function 总被引:3,自引:0,他引:3
G.?Q.?Wang Y.?Q.?BaiEmail author C.?Roos 《Journal of Mathematical Modelling and Algorithms》2005,4(4):409-433
Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity
and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed
primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended
the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple
kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this
kernel function, both with large- and small-updates. The complexity bounds are
and
, respectively, which are as good as those in the linear case.
Mathematics Subject Classifications (2000) 90C22, 90C31. 相似文献
8.
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way. 相似文献
9.
Polynomiality of an inexact infeasible interior point algorithm for semidefinite programming 总被引:3,自引:0,他引:3
In this paper we present a primal-dual inexact infeasible interior-point algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility to be maintained even if the initial iterate happened to be a feasible solution of the problem. Under a mild assumption on the inexactness, we show that the algorithm can find an -approximate solution of an SDP in O(n2ln(1/)) iterations. This bound of our algorithm is the same as that of the exact infeasible interior point algorithms proposed by Y. Zhang.Research supported in part by the Singapore-MIT alliance, and NUS Academic Research Grant R-146-000-032-112.Mathematics Subject Classification (1991): 90C05, 90C30, 65K05 相似文献
10.
Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.The research of this author was supported by an Overseas Research Scholarship of the Ministry of Education, Science and Culture of Japan.The research of this author was supported by National Science Foundation grants #DMS-9024622 and #DMS-9321938, North Atlantic Treaty Organization grant #CRG 920067, and an allocation of computing resources from the North Carolina Supercomputing Program.The research of this author was supported by North Atlantic Treaty Organization grant #CRG 920067. 相似文献