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51.
杨世国 《浙江大学学报(理学版)》2005,32(6):621-622,634
利用距离几何的理论与方法研究了n维欧氏空间En中n维单形的几何不等式问题,建立了垂足单形的两个新的几何不等式,作为其特例,得n维Euler不等式及其推广. 相似文献
52.
Two aspects of the multidimensional bisection algorithms for the global optimisation of Lipschitz continuous functions are investigated. Firstly, for several test functions we examine the numerical performance of the deepest point algorithm and two acceleration procedures. Secondly, we phrase the branch and bound framework of Horst and Tuy in terms of covers, and show the algorithms to be included in this framework. A result of Basso on the convergence of localisations is extended to higher dimensions.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990. 相似文献
53.
The dual simplex method for generalized upper bound (GUB) problems is presented. One of the major operations in the dual simplex method is to update the elements of therth row, wherer is the index for the leaving basic variable. Those updated elements are used for the ratio test to determine the entering basic variabble. A very simple formula for therth row update for the dual simplex method for a GUB problem is derived, which is similar to the formula for the standard linear program. This derivation is based on the change key operation, which is to exchange the key column and its counterpart in the nonkey section. The change key operation is possible because of a theorem that guarantees the existence of such a counterpart. 相似文献
54.
Robert Fourer 《Mathematical Programming》1992,53(1-3):213-235
The first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise-linear functions subject to linear constraints. This concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program. The advantages are shown to be implicit in relationships between the linear and piecewise-linear algorithms, and to be independent of many details of implementation. Two sets of computational results serve to illustarate these arguments; the piecewise-linear simplex algorithm is observed to run 2–6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program. Further support for the practical value of a good piecewise-linear programming algorithm is provided by a survey of many varied applications.This research has been supported in part by the National Science Foundation under grant DMS-8217261. 相似文献
55.
M. Sun 《Journal of Optimization Theory and Applications》1993,79(2):405-413
We introduce a revised simplex algorithm for solving a typical type of dynamic programming equation arising from a class of finite Markov decision processes. The algorithm also applies to several types of optimal control problems with diffusion models after discretization. It is based on the regular simplex algorithm, the duality concept in linear programming, and certain special features of the dynamic programming equation itself. Convergence is established for the new algorithm. The algorithm has favorable potential applicability when the number of actions is very large or even infinite. 相似文献
56.
This paper deals with a critical evaluation of various finite element models for low-viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least-squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low-viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least-squares method in conjunction with C1-continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least-squares method in combination with isoparmetric Hermite elements offers a new general-purpose modelling technique which can accurately simulate all types of low-viscosity incompressible laminar flow in complex domains. 相似文献
57.
Wang Jia 《Geometriae Dedicata》1998,70(1):49-56
We establish an identity for an n-dimensional simplex relating the circumradius and the inradius, and an identity relating its volume and the pedal volume. As applications, we derive some known inequalities for simplices and generalizations of such inequalities. 相似文献
58.
Sverre Storøy 《BIT Numerical Mathematics》1967,7(3):216-225
The present paper describes a simple method to find an indicator of the error in solutions found by a procedure using the simplex-technique, and also describes a method for improving these solutions to any desired accuracy provided certain conditions are met. 相似文献
59.
Erwin Lutwak 《Geometriae Dedicata》1997,66(1):119-124
The aim of this note is to strengthen and generalize an inequality of Sangwine–Yager regarding means of various quantities associated with the simplices circumscribing a convex body. 相似文献
60.
联系两个n维单形的一类不等式 总被引:1,自引:0,他引:1
本文给出了联系两个n维单形的一类不等式,从而推广和改进了文[1]、[2][3]的结论。 相似文献