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1.
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
2.
1引言在微重力下用浮区法生长高质量、大体积单晶体是一种很有应用前景的方法,但热毛细对流所引起的诸如宏观不均匀性、生长条纹等缺陷严重限制了这一方法的应用。目前,人们试着用液封方法抑制热毛细对流。文献[1~3]分别对两层流体系统内的热毛细对流所作的研究表明:通过液封,被封层内的热毛细对流可以得到显著抑制。本文对圆柱三层流体系统内的热毛细对流进行研究,为热毛细对流规律的揭示以及进一步总结出其控制方法提供了理论数值依据。2控制方程和边界条件考虑长为L的互不溶混的三层轴对称同轴液柱,如图1所示,两端壁保持定温T… 相似文献
3.
Dahui Luo JinRong Wang Dong Shen 《Mathematical Methods in the Applied Sciences》2019,42(13):4543-4553
This paper considers the consensus tacking problem for nonlinear fractional‐order multiagent systems by presenting a PDα‐type iterative learning control update law with initial learning mechanisms. The asymptotical convergence of the proposed distributed learning algorithm is strictly proved by using the properties of fractional calculus. A sufficient condition is derived to guarantee the whole multiagent system achieving an asymptotic output consensus. An illustrative example is given to verify the theoretical results. 相似文献
4.
由于时间序列数据中经常出现的厚尾特征使得通常的估计方法不再具有渐近的正态分布,在误差项二阶矩有限的条件下考虑了非线性自回归序列的L_1估计.采用局部线性近似的方法得到了具有凸样本路径的随机过程,在此基础上利用凸样本路径随机过程弱收敛的性质证明了非线性自回归序列L_1估计的渐近正态性及无偏性. 相似文献
5.
LIU Hong-Zhun PAN Zu-Liang LI Peng 《理论物理通讯》2006,46(10)
In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples. 相似文献
6.
§ 1 IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up, x∈ R,( 1 )where1
相似文献
7.
We study the equidistribution on spheres of the n-step transition probabilities of random walks on graphs. We give sufficient conditions for this property being satisfied and for the weaker property of asymptotical equidistribution. We analyze the asymptotical behaviour of the Green function of the simple random walk on 2 and we provide a class of random walks on Cayley graphs of groups, whose transition probabilities are not even asymptotically equidistributed. 相似文献
8.
One-dimensional perturbed neutral delay differential equations of the form (x(t)−P(t,x(t−τ)))′=f(t,xt)+g(t,xt) are considered assuming that f satisfies −v(t)M(φ)?f(t,φ)?v(t)M(−φ), where M(φ)=max{0,maxs∈[−r,0]φ(s)}. A typical result is the following: if ‖g(t,φ)‖?w(t)‖φ‖ and , then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation (x(t)−P(t,x(t−τ)))′=f(t,xt) is uniformly asymptotically stable. Some known results associated with this equation are extended and improved. 相似文献
9.
A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system. 相似文献
10.
The paper is concerned with the two-sample mean
testing problem in high-dimension settings. We propose a composite Hotelling's
T-square test, establish its asymptotical normality and study its local power.
The finite-sample priority of the proposed test over existing high-dimensional
tests is shown by simulations and illustrated by a real data-set analysis. 相似文献