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1.
Given D a domain in
, G an open set in
and E a subset of D verifying the harmonic analogue of Local Polynomial Condition of Leja at some point in D. We prove that if f(x, y) is a complex function defined on D × G such that– f(x, ) is harmonic on G for every fixed x E,– f(, y) is harmonic on D for every fixed y G,then f is harmonic in (x, y) on D × G. 相似文献
2.
S. P. Sidorov 《Numerical Algorithms》2007,44(3):273-279
Let , –1<x
1<...<x
n
<1. Denote , t∈(–1,1). Given a function f∈W we try to recover f(ζ) at fixed point ζ∈(–1,1) by an algorithm A on the basis of the information f(x
1),...,f(x
n
). We find the intrinsic error of recovery .
This work is supported by RFBR (grant 07-01-00167-a and grant 06-01-00003). 相似文献
3.
Copositive approximation of periodic functions 总被引:1,自引:0,他引:1
Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points y
i
∈ Y:= {y
i
}
i∈ℤ such that for x ∈ [y
i
, y
i−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each n ≧ N(Y) we construct a trigonometric polynomial P
n
of order ≦ n, changing its sign at the same points y
i
∈ Y as f, and
where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω
3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm.
This work was done while the first author was visiting CPT-CNRS, Luminy, France, in June 2006. 相似文献
4.
Convex programs with an additional reverse convex constraint 总被引:2,自引:0,他引:2
H. Tuy 《Journal of Optimization Theory and Applications》1987,52(3):463-486
A method is presented for solving a class of global optimization problems of the form (P): minimizef(x), subject toxD,g(x)0, whereD is a closed convex subset ofR
n
andf,g are convex finite functionsR
n
. Under suitable stability hypotheses, it is shown that a feasible point
is optimal if and only if 0=max{g(x):xD,f(x)f(
)}. On the basis of this optimality criterion, the problem is reduced to a sequence of subproblemsQ
k
,k=1, 2, ..., each of which consists in maximizing the convex functiong(x) over some polyhedronS
k
. The method is similar to the outer approximation method for maximizing a convex function over a compact convex set. 相似文献
5.
It is known that the problem of minimizing a convex functionf(x) over a compact subsetX of
n
can be expressed as minimizing max{g(x, y)|y X}, whereg is a support function forf[f(x) g(x, y), for ally X andf(x)=g(x, x)]. Standard outer-approximation theory can then be employed to obtain outer-approximation algorithms with procedures for dropping previous cuts. It is shown here how this methodology can be extended to nonconvex nondifferentiable functions.This research was supported by the Science and Engineering Research Council, UK, and by the National Science Foundation under Grant No. ECS-79-13148. 相似文献
6.
D. F. Miller 《Journal of Optimization Theory and Applications》2007,134(3):413-432
This paper develops boundary integral representation formulas for the second variations of cost functionals for elliptic domain
optimization problems. From the collection of all Lipschitz domains Ω which satisfy a constraint ∫
Ω
g(x) dx=1, a domain is sought which maximizes either
, fixed x
0∈Ω, or ℱ(Ω)=∫
Ω
F(x,u(x)) dx, where u solves the Dirichlet problem Δu(x)=−f(x), x∈Ω, u(x)=0, x∈∂Ω. Necessary and sufficient conditions for local optimality are presented in terms of the first and second variations of the
cost functionals
and ℱ. The second variations are computed with respect to domain variations which preserve the constraint. After first summarizing
known facts about the first variations of u and the cost functionals, a series of formulas relating various second variations of these quantities are derived. Calculating
the second variations depends on finding first variations of solutions u when the data f are permitted to depend on the domain Ω. 相似文献
7.
A generalized cutting-plane algorithm designed to solve problems of the form min{f(x) :x X andg(x,y) 0 for ally Y} is described. Convergence is established in the general case (f,g continuous,X andY compact). Constraint dropping is allowed in a special case [f,g(·,y) convex functions,X a convex set]. Applications are made to a variety of max-min problems. Computational considerations are discussed.Dr. Falk's research was supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Contract No. 73–2504. 相似文献
8.
Let X be a normed space and V be a convex subset of X. Let a\colon \mathbbR+ ? \mathbbR+{\alpha \colon \mathbb{R}_+ \to \mathbb{R}_+}. A function f \colon V ? \mathbbR{f \colon V \to \mathbb{R}} is called α-midconvex if
f (\fracx + y2)-\fracf(x) + f(y)2 £ a(||x - y||) for x, y ? V.f \left(\frac{x + y}{2}\right)-\frac{f(x) + f(y)}{2}\leq \alpha(\|x - y\|)\quad {\rm for} \, x, y \in V. 相似文献
9.
In Geoffroy et al, Acceleration of convergence in Dontchev's iterative method for solving variational inclusions Serdica Math. J. 29 (2003), pp. 45–54] we showed the convergence of a cubic method for solving generalized equations of the form 0 ∈ f(x) +- G(x) where f is a function and G stands for a set-valued map. We investigate here the stability of such a method with respect to some perturbations. More precisely, we consider the perturbed equation y ∈ f(x) +- G(x) and we show that the pseudo-Lipschitzness of the map (f +- G)−1 is closely tied to the uniformity of our method in the sense that the attraction region does not depend on small perturbations of the parameter y. Finally, we provide an enhanced version of the convergence theorem established by Geoffroy, et al. 相似文献
10.
Some minimax problems of vector-valued functions 总被引:2,自引:0,他引:2
T. Tanaka 《Journal of Optimization Theory and Applications》1988,59(3):505-524
The concepts of cone extreme points, cone saddle points, and cone saddle values are introduced. The relation of inclusion among the sets mini
xX
max
yY
f(x, y), maxi
yY
min
xX
f(x, y), and the set of all weak cone saddle values is investigated in the case where the image space
n
off is ordered by an acute convex cone.The author is grateful for the useful suggestions and comments given by Prof. K. Tanaka, Niigata University, Niigata, Japan.The author would like to thank the referees for their valuable suggestions on the original draft. 相似文献
11.
Giovanni Di Lena Davide Franco Mario Martelli Basilio Messano 《Mediterranean Journal of Mathematics》2011,8(4):473-489
The main purpose of this paper is to investigate dynamical systems
F : \mathbbR2 ? \mathbbR2{F : \mathbb{R}^2 \rightarrow \mathbb{R}^2} of the form F(x, y) = (f(x, y), x). We assume that
f : \mathbbR2 ? \mathbbR{f : \mathbb{R}^2 \rightarrow \mathbb{R}} is continuous and satisfies a condition that holds when f is non decreasing with respect to the second variable. We show that for every initial condition x0 = (x
0, y
0), such that the orbit
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