共查询到20条相似文献,搜索用时 19 毫秒
1.
Alysson M. Costa Jean-François Cordeau Bernard Gendron 《Computational Optimization and Applications》2009,42(3):371-392
Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like
relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities
that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated
to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays
to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities.
We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments
show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities. 相似文献
2.
In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures. 相似文献
3.
This work is concerned with exploring more refinement forms of the Young inequalities and the Kittaneh–Manasrah inequalities. We deduce the Operator version inequalities and reverse version inequalities related to the Kittaneh–Manasrah inequalities. 相似文献
4.
《Journal of Computational and Applied Mathematics》2005,182(2):316-326
In this paper, we introduce and consider a new class of variational inequalities, known as the hemivariational-like inequalities. It is shown that the hemivariational-like inequalities include hemivariational inequalities, variational-like inequalities and the classical variational inequalities as special cases. The auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational-like inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. 相似文献
5.
Javad Balooee 《Journal of Optimization Theory and Applications》2013,159(1):192-209
In this paper, we investigate or analyze non-convex variational inequalities and general non-convex variational inequalities. Two new classes of non-convex variational inequalities, named regularized non-convex variational inequalities and general regularized non-convex variational inequalities, are introduced, and the equivalence between these two classes of non-convex variational inequalities and the fixed point problems are established. A projection iterative method to approximate the solutions of general regularized non-convex variational inequalities is suggested. Meanwhile, the existence and uniqueness of solution for general regularized non-convex variational inequalities is proved, and the convergence analysis of the proposed iterative algorithm under certain conditions is studied. 相似文献
6.
Khaled Mehrez 《Integral Transforms and Special Functions》2017,28(2):130-144
In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function. 相似文献
7.
Robert Weismantel 《Mathematical Programming》1997,77(3):49-68
This paper deals with the 0/1 knapsack polytope. In particular, we introduce the class ofweight inequalities. This class of inequalities is needed to describe the knapsack polyhedron when the weights of the items lie in certain intervals.
A generalization of weight inequalities yields the so-called “weight-reduction principle” and the class of extended weight
inequalities. The latter class of inequalities includes minimal cover and (l,k)-configuration inequalities. The properties of lifted minimal cover inequalities are extended to this general class of inequalities. 相似文献
8.
Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer
programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities.?Given
a mixed-integer region S and a collection of valid “base” mixed-integer inequalities, we develop a procedure for generating new valid inequalities
for S. The starting point of our procedure is to consider the MIR inequalities related with the base inequalities. For any subset
of these MIR inequalities, we generate two new inequalities by combining or “mixing” them. We show that the new inequalities
are strong in the sense that they fully describe the convex hull of a special mixed-integer region associated with the base
inequalities.?We discuss how the mixing procedure can be used to obtain new classes of strong valid inequalities for various
mixed-integer programming problems. In particular, we present examples for production planning, capacitated facility location,
capacitated network design, and multiple knapsack problems. We also present preliminary computational results using the mixing
procedure to tighten the formulation of some difficult integer programs. Finally we study some extensions of this mixing procedure.
Received: April 1998 / Accepted: January 2001?Published online April 12, 2001 相似文献
9.
Karen Aardal 《Mathematical Programming》1998,81(2):149-175
We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack cover, flow cover, effective capacity, single depot, and combinatorial inequalities. The flow cover, effective capacity and single depot inequalities form subfamilies of the general family of submodular inequalities. The separation problem based on the family of submodular inequalities is NP-hard in general. For the well known subclass of flow cover inequalities, however, we show that if the client set is fixed, and if all capacities are equal, then the separation problem can be solved in polynomial time. For the flow cover inequalities based on an arbitrary client set and general capacities, and for the effective capacity and single depot inequalities we develop separation heuristics. An important part of these heuristics is based on the result that two specific conditions are necessary for the effective cover inequalities to be facet defining. The way these results are stated indicates precisely how structures that violate the two conditions can be modified to produce stronger inequalities. The family of combinatorial inequalities was originally developed for the uncapacitated facility location problem, but is also valid for the capacitated problem. No computational experience using the combinatorial inequalities has been reported so far. Here we suggest how partial output from the heuristic identifying violated submodular inequalities can be used as input to a heuristic identifying violated combinatorial inequalities. We report on computational results from solving 60 medium size problems. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. 相似文献
10.
We consider Hardy-Rellich inequalities and discuss their possible improvement. The procedure is based on decomposition into spherical harmonics, where in addition various new inequalities are obtained (e.g. Rellich-Sobolev inequalities). We discuss also the optimality of these inequalities in the sense that we establish (in most cases) that the constants appearing there are the best ones. Next, we investigate the polyharmonic operator (Rellich and higher order Rellich inequalities); the difficulties arising in this case come from the fact that (generally) minimizing sequences are no longer expected to consist of radial functions. Finally, the successively use of the Rellich inequalities lead to various new higher order Rellich inequalities. 相似文献
11.
In this paper, we introduce and study a class of differential vector variational inequalities in finite dimensional Euclidean spaces. We establish a relationship between differential vector variational inequalities and differential scalar variational inequalities. Under various conditions, we obtain the existence and linear growth of solutions to the scalar variational inequalities. In particular we prove existence theorems for Carathéodory weak solutions of the differential vector variational inequalities. Furthermore, we give a convergence result on Euler time-dependent procedure for solving the initial-value differential vector variational inequalities. 相似文献
12.
This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
13.
In a recent paper, Domokos and Kolumbán introduced variational inequalities with operator solutions to provide a suitable
unified approach to several kinds of variational inequality and vector variational inequality in Banach spaces. Inspired by
their work, in this paper, we further develop the new scheme of vector variational inequalities with operator solutions from
the single-valued case into the multi-valued one. We prove the existence of solutions of generalized vector variational inequalities
with operator solutions and generalized quasi-vector variational inequalities with operator solutions. Some applications to
generalized vector variational inequalities and generalized quasi-vector variational inequalities in a normed space are also
provided. 相似文献
14.
We examine linear inequalities satisfied by the
flag $f$-vectors of polytopes. One source of these inequalities
is the toric $g$-vector; convolutions of its entries are non-negative
for rational polytopes. We prove a conjecture of Meisinger about a
redundancy in these inequalities. Another source of inequalities is
the {\bf cd}-index; among all $d$-polytopes, each {\bf cd}-index coefficient
is minimized on the $d$-simplex. We show that not all of the {\bf cd}-index
inequalities are implied by the toric $g$-vector inequalities, and that not all of the toric $g$-vector inequalities are implied by the {\bf cd}-index
inequalities.
Finally, we show that some inequalities from
convolutions of {\bf cd}-index coefficients are implied by other
{\bf cd}-index inequalities. 相似文献
15.
Peter McMullen 《Monatshefte für Mathematik》1991,111(1):47-53
Removing the dependence on dimension of the inequalities between quermassintegrals resulting from the Aleksandrov-Fenchel inequalities leads to universal quadratic inequalities between intrinsic volumes, and to an inequality for the Wills functional. The inequalities correspond to equations which hold in the polytope algebra. 相似文献
16.
该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式. 相似文献
17.
We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities
are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature
of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting
coefficients, lifting of flow cover inequalities is computationally very demanding. We present a computationally efficient
way to lift flow cover inequalities based on sequence independent lifting techniques and give computational results that show
the effectiveness of our lifting procedures.
Received May 15, 1996 / Revised version received August 7, 1998
Published online June 28, 1999 相似文献
18.
Q. H. Ansari Z. Khan A. H. Siddiqi 《Journal of Optimization Theory and Applications》2005,127(2):263-283
In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities.
It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational
inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector
variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the
solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational
inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted
generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The
existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence
results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems
of generalized vector variational inequalities.
The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum
and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees
for comments and suggestions improving the final draft of this paper. 相似文献
19.
Lili Huan Biao Qu Jin-guang Jiang 《Journal of Applied Mathematics and Computing》2010,33(1-2):411-421
In this paper, we present some merit functions for general mixed quasi-variational inequalities, and we obtain the equivalent optimization problems to general mixed quasi-variational inequalities. Since the general mixed quasi-variational inequalities include general variational inequalities, quasi-variational inequalities and nonlinear (implicit) complementarity problems as special cases, our results continue to hold for these problems. In this respect, results obtained in this paper represent an extension of previously known results. 相似文献
20.
In this paper we introduce a new class of facet-inducing inequalities for the Windy Rural Postman Problem and the Windy General
Routing Problem. These inequalities are called Zigzag inequalities because they cut off fractional solutions containing a
zigzag associated with variables with 0.5 value. Two different types of inequalities, the Odd Zigzag and the Even Zigzag inequalities,
are presented. Finally, their application to other known Arc Routing Problems is discussed. 相似文献