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41.
郭飞 《应用数学与计算数学学报》1997,11(1):19-26
Wilson,Han和Powell提出的序列二次规划方法(简称SQP方法)是求解非线性规划问题的一个著名方法,这种方法每次迭代的搜索方向是通过求解一个二次规划子问题得到的,本文受[1]启发,得到二次规划子问题的一个近似解,进而给出了一类求解线性约束非线性规划问题的可行方向法,在约束集合满足正则性的条件下,证明了该算法对五种常用线性搜索方法具有全局收敛性。 相似文献
42.
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
43.
44.
Wei Wang Li-Ping Pang Zun-Quan Xia 《应用数学学报(英文版)》2007,23(1):29-38
In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given. 相似文献
45.
Poisson回归模型广泛应用于分析计数型数据 ,Dean&Lawless(1989)和Dean(1992 )讨论了非重复测量得到的计数型数据的偏大离差存在性的检验问题 .本文分别利用随机系数模型和对数非线性模型讨论了基于重复测量得到的计数型数据的偏大离差的检验问题 ,得到了检验的score统计量 . 相似文献
46.
Devin Kilminster David Allingham Alistair Mees 《Annals of the Institute of Statistical Mathematics》2002,54(1):224-233
Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data. 相似文献
47.
Ying Zhang Gang Hu Shigang Chen H.A. Cerdeira 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):381-384
A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the
well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a
wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The
system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust
against small external noise. The mechanism underlying this high control efficiency is intuitively explained.
Received 15 January 2002 Published online 6 June 2002 相似文献
48.
THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES 总被引:1,自引:0,他引:1
Wen Li Jian-xin Chen 《计算数学(英文版)》2006,24(2):141-148
In this paper we present some new absolute and relative perturbation bounds for theeigenvalue for arbitrary matrices, which improves some recent results. The eigenvalueinclusion region is also discussed. 相似文献
49.
High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting
the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of
the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation
problems are taken into account to emphasize the main features of the proposed methods.
AMS subject classification (2000) 65L10, 65L12, 65L50 相似文献
50.
唐荣荣 《高校应用数学学报(A辑)》2006,21(4):413-418
利用渐近理论,讨论了一类非线性对偶系统.在适当的条件下,得出了这一类非线性系统解的存在性条件及其渐近解.将此结果用于二自由度陀螺系统,较简捷地得到了该系统的具有小而有限振幅的渐近解. 相似文献