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91.
H. Hu 《Journal of Global Optimization》2003,25(2):237-242
This paper studies the existence of a uniform global error bound when a convex inequality g 0, where g is a closed proper convex function, is perturbed. The perturbation neighborhoods are defined by small arbitrary perturbations of the epigraph of its conjugate function. Under certain conditions, 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 g satisfies the Slater condition and the solution set is bounded or its recession function satisfies the Slater condition. The results are used to derive lower bounds on the distance to ill-posedness. 相似文献
92.
Regina Sandra Burachik B. F. Svaiter 《Proceedings of the American Mathematical Society》2003,131(8):2379-2383
Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.
The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.
93.
We address the problem of finding the worst possible traffic a
user of a telecommunications network can send.
We take worst to mean having the highest effective
bandwidth, a concept that arises in the Large Deviation theory of
queueing networks.
The traffic is assumed to be stationary and to satisfy leaky bucket
constraints, which represent the a priori knowledge the network
operator has concerning the traffic.
Firstly, we show that this optimization problem may be reduced to an
optimization over periodic traffic sources.
Then, using convexity methods, we show that the realizations of a
worst case source must have the following properties:
at each instant the transmission rate must be either zero,
the peak rate, or the leaky bucket rate; it may only be the latter when
the leaky bucket is empty or full;
each burst of activity must either start with the leaky
bucket empty or end with it full. 相似文献
94.
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2003,284(2):775-778
Let X be a real Banach space. Let be a family of closed, convex subsets of X. We show that either the intersection ?γ∈Γ(Gγ)? of the ?-neighborhood of the sets Gγ is bounded for each ?>0, or it is unbounded for each ?>0. From this we derive a fixed point theorem for suitable maps that move some points along a bounded direction in Hilbert spaces. 相似文献
95.
In this paper we consider a new class of continuous location problems where the distances are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where there exist zero-distance regions. We prove a geometrical characterization of these measures of distance as the length of shortest paths between points using only a subset of directions of their unit balls. We also characterize the complete set of optimal solutions for this class of continuous single facility location problems and we give resolution methods to solve them. Our analysis allows to consider new models of location problems and generalizes previously known results. 相似文献
96.
A set X of boundary points of a (possibly unbounded) convex body KE
d illuminating K from within is called primitive if no proper subset of X still illuminates K from within. We prove that for such a primitive set X of an unbounded, convex set KE
d (distinct from a cone) one has X=2 if d=2, X6 if d=3, and that there is no upper bound for X if d4. 相似文献
97.
Peter Abramenko 《Journal of Combinatorial Theory, Series A》2010,117(4):440-453
We show that, if a building is endowed with its complete system of apartments, and if each panel is contained in at least four chambers, then the intersection of two apartments can be any convex subcomplex contained in an apartment. This combinatorial result is particularly interesting for lower-dimensional convex subcomplexes of apartments, where we definitely need the assumption on the four chambers per panel in the building. The corresponding statement is not true anymore for arbitrary systems of apartments, and counter-examples for infinite convex subcomplexes exist for any type of buildings. However, when we restrict to finite convex subcomplexes, the above remains true for arbitrary systems of apartments if and only if every finite subset of chambers of the standard Coxeter complex is contained in the convex hull of two chambers. 相似文献
98.
The main purpose of this paper is to complete the works presented by Andrieux and Varé (2002) and El Arem et al. (2003) by taking into account the effects of shearing in the constitutive equations of a beam cracked section in bi-axial flexure. The paper describes the derivation of a lumped cracked beam model from the three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips. Properties of the potential energy and convex analysis are used to reduce the three-dimensional computations needed for the model identification, and to derive the final form of the elastic energy that determines the nonlinear constitutive equations of the cracked transverse section. We aim to establish a relation of behavior between the applied forces and the resulting displacements field vectors, which is compatible with the beams theory in order to allow the model exploitation for shafts dynamics analysis. The approach has been applied to the case of a cracked beam with a single crack covering the half of its circular cross section. 相似文献
99.
In this article, we obtain some results about the mean curvature integrals of the parallel body of a convex set in R^n. These mean curvature integrals are generalizations of the Santalo's results. 相似文献
100.
Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements. 相似文献