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231.
This paper gives characterizations of optimal solutions to the nondifferentiable convex semi-infinite programming problem,
which involve the notion of Lagrangian saddlepoint. With the aim of giving the necessary conditions for optimality, local
and global constraint qualifications are established. These constraint qualifications are based on the property of Farkas-Minkowski,
which plays an important role in relation to certain systems obtained by linearizing the feasible set. It is proved that Slater's
qualification implies those qualifications. 相似文献
232.
《Journal of Quantitative Spectroscopy & Radiative Transfer》2004,86(2):133-150
We come back to a nonlinear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab. 相似文献
233.
The relation of two mathematical programs—the so-called primal, (P) and dual, (D)—Are studied when (P) is a maximization of the minimum of two functions and (D) is the minimization of the maximum of two functions, and the function-pair of (D) are derived by certain, conjugate-like operators from that of (P). It is demonstrated that the weak duality holds when at least one of the pair is continuous. When further premises are met the strong duality is proved. From these results the usual Fenchel-duality may be deducted as well as few other primal-dual pairs. 相似文献
234.
本文引入固定设计情形下回归函数小波估计的泛相合性概念,证明了此小波估计的泛相合性。 相似文献
235.
A new brief proof of Fan's minimax theorem for convex-concave like functions is established using separation arguments. 相似文献
236.
A. Liakopoulos 《国际流体数值方法杂志》1985,5(1):81-97
The applicability of a finite element-differential method to the computation of steady two-dimensional low-speed, transonic and supersonic turbulent boundary-layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the K-? two-equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial-value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k-? turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good. 相似文献
237.
Satoru Fujishige 《Mathematical Programming》1984,29(3):348-360
The author recently introduced a concept of a subdifferential of a submodular function defined on a distributive lattice. Each subdifferential is an unbounded polyhedron. In the present paper we determine the set of all the extreme points and rays of each subdifferential and show the relationship between subdifferentials of a submodular function and subdifferentials, in an ordinary sense of convex analysis, of Lovász's extension of the submodular function. Furthermore, for a modular function on a distributive lattice we give an algorithm for determining which subdifferential contains a given vector and finding a nonnegative linear combination of extreme vectors of the subdifferential which expresses the given vector minus the unique extreme point of the subdifferential. 相似文献
238.
Satoru Fujishige 《Mathematical Programming》1984,29(2):125-141
The present paper shows that for any submodular functionf on a crossing family
with
, if the polyhedron
is nonempty, then there exist a unique distributive lattice
with
and a unique submodular function
with
such thatB(f) coincides with the base polyhedron
associated with the submodular system
. Here, iff is integer-valued, thenf
1 is also integer-valued.
Based on this fact, we also show the relationship between the independent-flow problem considered by the author and the minimum
cost flow problem considered by J. Edmonds and R. Giles. 相似文献
239.
《复变函数与椭圆型方程》2012,57(5):441-445
It is well known that the q-Gamma function cannot be characterised by its functional equation o q ( z + 1) =/((1 m q z )(1 m q )) o q ( z ) and the condition o q (1) = 1. In 1980 Richard Askey showed in [1] that the additional assumption of logarithmic convexity yields the uniqueness of o q ( x ) for real x > 0. The goal of this note is to establish a q-extension of Wielandt's theorem which gives a characterization of o q ( z ) for all $ z\in \{z\in{\shadC}:{\rm Re}(z)\gt 0\} $ . 相似文献
240.
《复变函数与椭圆型方程》2012,57(8):653-662
It is shown how Clifford analysis offers a natural framework for defining the principal value kernel in euclidean m -dimensional space. Some elegant generalizations of classical formulae on the real line are obtained. 相似文献