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891.
Lipschitzian optimization without the Lipschitz constant 总被引:30,自引:0,他引:30
D. R. Jones C. D. Perttunen B. E. Stuckman 《Journal of Optimization Theory and Applications》1993,79(1):157-181
We present a new algorithm for finding the global minimum of a multivariate function subject to simple bounds. The algorithm is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. This is done by carrying out simultaneous searches using all possible constants from zero to infinity. On nine standard test functions, the new algorithm converges in fewer function evaluations than most competing methods.The motivation for the new algorithm stems from a different way of looking at the Lipschitz constant. In particular, the Lipschitz constant is viewed as a weighting parameter that indicates how much emphasis to place on global versus local search. In standard Lipschitzian methods, this constant is usually large because it must equal or exceed the maximum rate of change of the objective function. As a result, these methods place a high emphasis on global search and exhibit slow convergence. In contrast, the new algorithm carries out simultaneous searches using all possible constants, and therefore operates at both the global and local level. Once the global part of the algorithm finds the basin of convergence of the optimum, the local part of the algorithm quickly and automatically exploits it. This accounts for the fast convergence of the new algorithm on the test functions. 相似文献
892.
Quasi—Einstein Hypersurfaces in a Hyperbolic Space 总被引:1,自引:0,他引:1
§1. IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj, (i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1… 相似文献
893.
894.
Tsugunori Nogura 《Topology and its Applications》1983,15(1):65-69
We study the question whether a topological space X with a property can be embedded in a countably compact space X? with the same property . 相似文献
895.
Frank Caridi 《Journal of multivariate analysis》1983,13(1):52-66
For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes. 相似文献
896.
In this paper, we consider the hypersurfaces of Randers space with constant flag curvature. (1) Let (Mn+1, F) be a Randers-Minkowski space. If (Mn, F) is a hypersurface of (Mn+1, F) with constant flag curvature K=1, then we can prove that M is Riemannian. (2) Let (Mn+1, F) be a Randers space with constant flag curvature. Assume (M, F) is a compact hypersurface of (Mn+1, F) with constant mean curvature|H|. Then a pinching theorem is established, which generalizes the result of[Proc. Amer. Math. Soc., 120, 1223-1229 (1994)] from the Riemannian case to the Randers space. 相似文献
897.
898.
A.F Gualtierotti 《Journal of multivariate analysis》1974,4(3):347-349
We consider the notion of a spherically invariant measure on a real and separable Hilbert space and study some equivalence properties of measures of this type. The latter are of interest in statistical communication theory. 相似文献
899.
900.
The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors. 相似文献