共查询到20条相似文献,搜索用时 15 毫秒
1.
Asymptotic constraint qualifications and global error bounds for convex inequalities 总被引:2,自引:0,他引:2
Received October 26, 1996 / Revised version received October 1, 1997 Published online October 9, 1998 相似文献
2.
Global error bounds with fractional exponents 总被引:2,自引:0,他引:2
Using the partial order induced by a proper weakly lower semicontinuous function on a reflexive Banach space X we give a sufficient condition for f to have error bounds with fractional exponents. Application is given to identify the set of such exponents for quadratic
functions.
Received: August 20, 1999 / Accepted: March 20, 2000?Published online July 20, 2000 相似文献
3.
H. Hu 《Mathematical Programming》2000,88(2):277-284
This paper studies the existence of a uniform global error bound when a system of linear inequalities is under local arbitrary
perturbations. Specifically, given a possibly infinite system of linear inequalities satisfying the Slater’s condition and
a certain compactness condition, it is shown that for sufficiently small arbitrary perturbations the perturbed system is solvable
and there exists a uniform global error bound if and only if the original system is bounded or its homogeneous system has
a strict solution.
Received: April 12, 1998 / Accepted: February 11, 2000?Published online July 20, 2000 相似文献
4.
In this paper, we give some characterizations of linear and nonlinear error bounds for lower semicontinuous functions by a new notion, called subslope. And, extend some results of Azé and Corvellec (SIAM J Optim 12:913–927, 2002) and Corvellec and Motreanu (Math Program Ser A 114:291–319, 2008) slightly. Furthermore, we get a sufficient and necessary condition for global linear error bounds. 相似文献
5.
The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic
approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational
results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem
by Martello and Toth, which can be understood as a special case. In particular, we prove an asymptotic worst-case performance
of 3/4 for a bound that can be computed in linear time for items sorted by size. In addition, our approach provides a general
framework for establishing new bounds.
Received: August 11, 1998 / Accepted: February 1, 2001?Published online September 17, 2001 相似文献
6.
As a development of the theory of linear error bounds for lower semicontinuous functions defined on complete metric spaces,
introduced in Azé et al. (Nonlinear Anal 49, 643–670, 2002) and refined in Azé and Corvellec (ESAIM Control Optim Calc Var 10, 409–425, 2004), we propose a similar approach to nonlinear error bounds, based on the notion of strong slope, the variational
principle, and the change-of-metric principle, the latter allowing to obtain sharp estimates for such error bounds through
a reduction to the linear case. 相似文献
7.
We obtain local estimates of the distance to a set defined by equality constraints under assumptions which are weaker than
those previously used in the literature. Specifically, we assume that the constraints mapping has a Lipschitzian derivative,
and satisfies a certain 2-regularity condition at the point under consideration. This setting directly subsumes the classical
regular case and the twice differentiable 2-regular case, for which error bounds are known, but it is significantly richer
than either of these two cases. When applied to a certain equation-based reformulation of the nonlinear complementarity problem,
our results yield an error bound under an assumption more general than b-regularity. The latter appears to be the weakest assumption under which a local error bound for complementarity problems
was previously available. We also discuss an application of our results to the convergence rate analysis of the exterior penalty
method for solving irregular problems.
Received: February 2000 / Accepted: November 2000?Published online January 17, 2001 相似文献
8.
We consider the parametric programming problem (Q
p
) of minimizing the quadratic function f(x,p):=x
T
Ax+b
T
x subject to the constraint Cx≤d, where x∈ℝ
n
, A∈ℝ
n×n
, b∈ℝ
n
, C∈ℝ
m×n
, d∈ℝ
m
, and p:=(A,b,C,d) is the parameter. Here, the matrix A is not assumed to be positive semidefinite. The set of the global minimizers and the set of the local minimizers to (Q
p
) are denoted by M(p) and M
loc
(p), respectively. It is proved that if the point-to-set mapping M
loc
(·) is lower semicontinuous at p then M
loc
(p) is a nonempty set which consists of at most ?
m,n
points, where ?
m,n
= is the maximal cardinality of the antichains of distinct subsets of {1,2,...,m} which have at most n elements. It is proved also that the lower semicontinuity of M(·) at p implies that M(p) is a singleton. Under some regularity assumption, these necessary conditions become the sufficient ones.
Received: November 5, 1997 / Accepted: September 12, 2000?Published online November 17, 2000 相似文献
9.
For the extended linear complementarity problem over an affine subspace, we first study some characterizations of (strong)
column/row monotonicity and (strong) R
0-property. We then establish global s-type error bound for this problem with the column monotonicity or R
0-property, especially for the one with the nondegeneracy and column monotonicity, and give several equivalent formulations
of such error bound without the square root term for monotone affine variational inequality. Finally, we use this error bound
to derive some properties of the iterative sequence produced by smoothing methods for solving such a problem under suitable
assumptions.
Received: May 2, 1999 / Accepted: February 21, 2000?Published online July 20, 2000 相似文献
10.
AbstractIn this article, our main aim is to develop gap functions and error bounds for a (non-smooth) convex vector optimization problem. We show that by focusing on convexity we are able to quite efficiently compute the gap functions and try to gain insight about the structure of set of weak Pareto minimizers by viewing its graph. We will discuss several properties of gap functions and develop error bounds when the data are strongly convex. We also compare our results with some recent results on weak vector variational inequalities with set-valued maps, and also argue as to why we focus on the convex case. 相似文献
11.
12.
The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang &; Pang's result [30], on error bound of Hölderian type. The results in the present paper generalize and unify recent works by Luo &; Luo in [17], Li in [16] and Wang &; Pang in [30]. 相似文献
13.
We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on
the right–hand–side and has a multivariate Gaussian distribution. Computation of these bounds requires the solution of only
as many linear programs as the problem has variables.
Received December 2, 1997 / Revised version received January 5, 1999? Published online May 12, 1999 相似文献
14.
Error bounds for proximal point subproblems and associated inexact proximal point algorithms 总被引:1,自引:0,他引:1
We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem,
and of the closely related problem of finding a zero of a maximal monotone operator. A new merit function is proposed for
proximal point subproblems associated with the latter. This merit function is based on Burachik-Iusem-Svaiter’s concept of
ε-enlargement of a maximal monotone operator. For variational inequalities, we establish a precise relationship between the
regularized gap function, which is a natural error measure in this context, and our new merit function. Some error bounds
are derived using both merit functions for the corresponding formulations of the proximal subproblem. We further use the regularized
gap function to devise a new inexact proximal point algorithm for solving monotone variational inequalities. This inexact
proximal point method preserves all the desirable global and local convergence properties of the classical exact/inexact method,
while providing a constructive error tolerance criterion, suitable for further practical applications. The use of other tolerance
rules is also discussed.
Received: April 28, 1999 / Accepted: March 24, 2000?Published online July 20, 2000 相似文献
15.
黄辉 《高校应用数学学报(A辑)》2007,22(1):74-80
考虑了伪凸集值映射的误差界.证明了对于伪凸集值映射,局部误差界成立意味着整体误差界成立.通过相依导数,给出了伪凸集值映射存在误差界的一些等价叙述. 相似文献
16.
YEMAODONG 《高校应用数学学报(英文版)》1998,13(2):223-230
In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained. 相似文献
17.
L. C. Zhao 《Journal of multivariate analysis》1989,29(2)
Let (X, Y), (X1, Y1), …, (Xn, Yn) be i.d.d. Rr × R-valued random vectors with E|Y| < ∞, and let Qn(x) be a kernel estimate of the regression function Q(x) = E(Y|X = x). In this paper, we establish an exponential bound of the mean deviation between Qn(x) and Q(x) given the training sample Zn = (X1, Y1, …, Xn, Yn), under conditions as weak as possible. 相似文献
18.
Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998 相似文献
19.
黄辉 《高校应用数学学报(A辑)》2003,18(3):357-364
考虑了凸集值映射的整体误差界,推广Li和Singer(1998)的主要定理到无界情形并肯定地回答了该文的猜想.作为应用,给出了线性Hoffman误差界定理一个简单的新证明. 相似文献
20.
In this paper, we study error bounds for lower semicontinuous functions defined on Banach space and linear regularity for finitely many closed subset in Banach spaces. By using Clarke's subd- ifferentials and Ekeland variational principle, we establish several sufficient conditions ensuring error bounds and linear regularity in Banach spaces. 相似文献