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1.
针对两个可分凸函数的和在线性约束下的极小化问题,在交替方向法的框架下,提出广义的交替近似梯度算法.在一定的条件下,该算法具有全局及线性收敛性.数值实验表明该算法有好的数值表现. 相似文献
2.
S. T. Glad 《Journal of Optimization Theory and Applications》1979,28(2):135-156
The convergence properties of different updating methods for the multipliers in augmented Lagrangians are considered. It is assumed that the updating of the multipliers takes place after each line search of a quasi-Newton method. Two of the updating methods are shown to be linearly convergent locally, while a third method has superlinear convergence locally. Modifications of the algorithms to ensure global convergence are considered. The results of a computational comparison with other methods are presented.This work was supported by the Swedish Institute of Applied Mathematics. 相似文献
3.
《Optimization》2012,61(10):1729-1743
ABSTRACTIn this note, we consider three types of problems, H-weighted nearest correlation matrix problem and two types of important doubly non-negative semidefinite programming, derived from the binary integer quadratic programming and maximum cut problem. The dual of these three types of problems is a 3-block separable convex optimization problem with a coupling linear equation constraint. It is known that, the directly extended 3-block alternating direction method of multipliers (ADMM3d) is more efficient than many of its variants for solving these convex optimization, but its convergence is not guaranteed. By choosing initial points properly, we obtain the convergence of ADMM3d for solving the dual of these three types of problems. Furthermore, we simplify the iterative scheme of ADMM3d and show the equivalence of ADMM3d to the 2-block semi-proximal ADMM for solving the dual's reformulation, under these initial conditions. 相似文献
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L. Contesse-Becker 《Journal of Optimization Theory and Applications》1993,79(2):273-310
In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile). 相似文献
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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical
convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations
between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions,
lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation
theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem
is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical
convergence by the help of modulus of continuity of positive linear operators are studied.
相似文献
9.
Ying-guang ShiDepartment of Mathematics Hunan Normal University Changsha China & Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,(2)
Abstract Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in theWeighted L~p norm on an arbitrary system of nodes are given. 相似文献
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The classical method for optimizing a functional subject to an integral constraint is to introduce the Lagrange multiplier and apply the Euler-Lagrange equations to the augmented integrand. The Lagrange multiplier is a constant whose value is selected such that the integral constraint is satisfied. This value is frequently an eigenvalue of the boundary-value problem and is determined by a trial-and-error procedure. A new approach for solving this isoperimetric problem is presented. The Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimum solution. A numerical example is given and is shown to have a large region of convergence. 相似文献
12.
本文对函数空间上的一致收敛拓扑、紧收敛拓扑及 Cauchy收敛拓扑之间的关系进行了讨论 ,给出了这三个拓扑间两两等价的充要条件 相似文献
13.
We present the geometric construction of some classical iterative methods that have global convergence and “infinite” speed of convergence when they are applied to solve certain nonlinear equations f(t)=0. In particular, for nonlinear equations with the degree of logarithmic convexity of f′, Lf′(t)=f′(t)f?(t)/f″(t)2, is constant, a family of Newton-type iterative methods of high orders of convergence is constructed. We see that this family of iterations includes the classical iterative methods. The convergence of the family is studied in the real line and the complex plane, and domains of semilocal and global convergence are located. 相似文献
14.
Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables 下载免费PDF全文
In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence. 相似文献
15.
Ahmed Roubi 《Computational Optimization and Applications》2001,19(3):319-335
Huard's method of centers is a method that solves constrained convex problems by means of unconstrained problems. In this paper we give some properties of this method, we analyse its convergence and rate of convergence and suggest some other variants and techniques to improve the speed of convergence. 相似文献
16.
The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LB
k
, UB
k
] including*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LB
k
and UB
k
allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.This research was supported by NSERC (Grant A8312) and FCAR (Grant 0899). 相似文献
17.
Ying-guang Shi 《应用数学学报(英文版)》2002,18(2):277-288
Abstract
Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted L
p
norm on an arbitrary system of nodes are given.
Supported by the National Natural Sciences Foundation of China (No.19671082) 相似文献
18.
史应光 《数学物理学报(B辑英文版)》2001,(1)
1 IntroductionThis paper deals with the uniform collvergence of truncated Hermte illterpolatioll oll anarbitrary systelll of 11odes. Tl1e mean collvergellce of trllllcated Herntite interpolation oll a11arbitrary syste12l of 1lodes 1las been st11died recently by tlle al1t11or[31. The converge11ce oftruncated Hern1ite illterpolatiou on tl1e zeros of the Jacobi polynontials is discussed in both tlleweigl1ted LP and the unfform norm by P. Vertesi and Y. X.[61.First we iutroduce some defi11itio… 相似文献
19.
本文研究了i.i.d情况下非参数回归的误差密度估计的一致收敛和均方收敛,给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。 相似文献
20.
Ahmed Roubi 《Computational Optimization and Applications》1994,3(3):259-280
We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems. 相似文献