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1.
A nonsmooth version of Newton's method 总被引:68,自引:0,他引:68
Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC
2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.This author's work is supported in part by the Australian Research Council.This author's work is supported in part by the National Science Foundation under grant DDM-8721709. 相似文献
2.
3.
一类二阶非线性阻尼微分方程的振动性 总被引:34,自引:0,他引:34
研究了一类二阶非线性阻尼微分方程解的振动性,建立了三个新的振动性定理,推广了Cecchi M和Marini M(Rocky Mount J Math,1992,22:1259-1276)的结果. 相似文献
4.
本文研究了两类边界条件下有振动系数的脉冲时滞抛物型方程解的振动性,得到了若干解振动的判别准则。其结果即使用于有固定符号系数的方程,也显著地改进了已有的结果。 相似文献
5.
The approximation power of moving least-squares 总被引:27,自引:0,他引:27
David Levin. 《Mathematics of Computation》1998,67(224):1517-1531
A general method for near-best approximations to functionals on , using scattered-data information is discussed. The method is actually the moving least-squares method, presented by the Backus-Gilbert approach. It is shown that the method works very well for interpolation, smoothing and derivatives' approximations. For the interpolation problem this approach gives Mclain's method. The method is near-best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation. The interpolation approximation in is shown to be a function, and an approximation order result is proven for quasi-uniform sets of data points.
6.
Flow past a stretching plate 总被引:24,自引:0,他引:24
Lawrence J. Crane 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(4):645-647
Zusammenfassung Eine Platte aus plastischem Material fliesst aus einem Spalt mit einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist. Eine exakte Lösung der Grenzschichtgleichungen für die von der Platte erzeugte Luftbewegung wird gegeben. Oberflächenreibung und Wärmeleitungskoeffizient werden berechnet. 相似文献
7.
Another note on Weyl's theorem 总被引:24,自引:0,他引:24
``Weyl's theorem holds" for an operator on a Banach space when the complement in the spectrum of the ``Weyl spectrum" coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the ``Browder spectrum", which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in . In this note we try to explore these distinctions.
8.
DISRUPTION MANAGEMENT FOR SUPPLY CHAIN COORDINATION WITH EXPONENTIAL DEMAND FUNCTION 总被引:24,自引:0,他引:24
The coordination problem of a supply chain comprising one supplier and one retailer under market demand disruption is studied in this article. A novel exponential demand function is adopted, and the penalty cost is introduced explicitly to capture the deviation production cost caused by the market demand disruption. The optimal strategies are obtained for different disruption scale under the centralized mode. For the decentralized mode, it is proved that the supply chain can be fully coordinated by adjusting the price discount policy appropriately when disruption occurs. Furthermore, the authors point out that similar results can be established for more general demand functions that represent different market circumstances if certain assumptions are satisfied. 相似文献
9.
Approximation by translates of refinable functions 总被引:23,自引:0,他引:23
Summary.
The functions
are
refinable if they are
combinations of the rescaled and translated functions
.
This is very common in scientific computing on a regular mesh.
The space of approximating functions with meshwidth
is a
subspace of with meshwidth
.
These refinable spaces have refinable basis functions.
The accuracy of the computations
depends on , the
order of approximation, which is determined by the degree of
polynomials
that lie in .
Most refinable functions (such as scaling functions in the theory
of wavelets) have no simple formulas.
The functions
are known only through the coefficients
in the refinement equation – scalars in the traditional case,
matrices for multiwavelets.
The scalar "sum rules" that determine
are well known.
We find the conditions on the matrices
that
yield approximation of order
from .
These are equivalent to the Strang–Fix conditions on the Fourier
transforms
, but for refinable
functions they can be explicitly verified from
the .
Received
August 31, 1994 / Revised version received May 2, 1995 相似文献
10.
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities 总被引:23,自引:0,他引:23
The smoothing Newton method for solving a system of nonsmooth equations , which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the th step, the nonsmooth function is approximated by a smooth function , and the derivative of at is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global convergence and convenience in handling. In this paper, we show that the smoothing Newton method is also superlinearly convergent if is semismooth at the solution and satisfies a Jacobian consistency property. We show that most common smooth functions, such as the Gabriel-Moré function, have this property. As an application, we show that for box constrained variational inequalities if the involved function is -uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).