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1.
We study several ways of obtaining valid inequalities for mixed integer programs. We show how inequalities obtained from a disjunctive argument can be represented by superadditive functions and we show how the superadditive inequalities relate to Gomory's mixed integer cuts. We also show how all valid inequalities for mixed 0–1 programs can be generated recursively from a simple subclass of the disjunctive inequalities.The research of this author was supported by NSF Contract No. ECS-8540898. 相似文献
2.
In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence of the effectiveness of including these inequalities as cuts in a Branch & Cut algorithm. 相似文献
3.
Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2006,318(1):53-62
In this paper, we consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known results. Since the general variational inequalities include the quasi-variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems. 相似文献
4.
Marek和Szyld建立了有界线性算子非负分裂的比较定理.他们还提出了严格不等式成立的条件,但没有进行详细证明.本注记首先用几个反例说明那里的保证严格不等式成立的条件是不充分的,然后给出正确的关于严格不等式的比较定理. 相似文献
5.
Arcadii Z. Grinshpan 《Journal of Mathematical Analysis and Applications》2008,338(2):1418-1430
We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given. 相似文献
6.
《Quaestiones Mathematicae》2013,36(7):985-1003
AbstractMathematical inequalities and other results involving such widely- and extensively-studied special functions of mathematical physics and applied mathematics as (for example) the Bessel, Struve and Lommel functions as well as the associated hypergeometric functions are potentially useful in many seemingly diverse areas of applications, especially in situations in which these functions are involved in solutions of mathematical, physical and engineering problems which can be modeled by ordinary and partial di?erential equations. With this objective in view, our present investigation is motivated by some open problems involving inequalities for a number of particular forms of the hypergeometric function 1F2(a; b, c; z). Here, in this paper, we apply a novel approach to such problems and obtain presumably new two-sided inequalities for the Struve function, the associated Struve function and the modified Struve function by first investigating inequalities for the general hypergeometric function 1F2(a; b, c; z). We also briefly discuss the analogous new inequalities for the Lommel function under some conditions and constraints. Finally, as special cases of our main results, we deduce several inequalities for the modified Lommel function and the normalized Lommel function. 相似文献
7.
Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To generate such inequalities, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We present new exact and heuristic separation algorithms for several classes of inequalities, namely lifted cover, extended cover, weight and lifted pack inequalities. Moreover, we show how to improve a recent separation algorithm for the 0-1 knapsack polytope itself. Extensive computational results, on MIPLIB and OR Library instances, show the strengths and limitations of the inequalities and algorithms considered. 相似文献
8.
9.
Mohammed Mesk 《Integral Transforms and Special Functions》2018,29(5):402-416
It is shown that the main inequality for several special functions derived in [Masjed-Jamei M. A main inequality for several special functions. Comput Math Appl. 2010;60:1280–1289] can be put in a concise form, and that the main inequalities of the first kind Bessel function, Laplace and Fourier transforms are not valid as presented in the aforementioned paper. To provide alternative inequalities, we give a generalization, being in some cases an improvement, of the Cauchy–Bunyakovsky–Schwarz inequality which can be applied to real functions not necessarily of constant sign. The corresponding discrete inequality is also obtained, which we use to improve the inequalities of the Riemann zeta and the generalized Hurwitz–Lerch zeta functions. Finally, from the main concise inequality, we derive a Turán-type inequality. 相似文献
10.
A. Taghavi V. Darvish H. M. Nazari S. S. Dragomir 《Annali dell'Universita di Ferrara》2017,63(2):377-389
In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results. 相似文献
11.
A new notion of partition‐determined functions is introduced, and several basic inequalities are developed for the entropies of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these functions. Here a compound set means a set obtained by varying each argument of a function of several variables over a set associated with that argument, where all the sets are subsets of an appropriate algebraic structure so that the function is well defined. On the one hand, the entropy inequalities developed for partition‐determined functions imply entropic analogues of general inequalities of Plünnecke‐Ruzsa type. On the other hand, the cardinality inequalities developed for compound sets imply several inequalities for sumsets, including for instance a generalization of inequalities proved by Gyarmati, Matolcsi and Ruzsa (2010). We also provide partial progress towards a conjecture of Ruzsa (2007) for sumsets in nonabelian groups. All proofs are elementary and rely on properly developing certain information‐theoretic inequalities. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 399–424, 2012 相似文献
12.
Gérard Cornuéjols 《Mathematical Programming》2008,112(1):3-44
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from
polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project
cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships
between these families. The tutorial also discusses computational aspects of generating the cuts and their strength.
Supported by NSF grant DMI-0352885, ONR grant N00014-03-1-0188 and ANR grant BLAN06-1-138894. 相似文献
13.
The article builds on several recent advances in the Monge-
Kantorovich theory of mass transport which have, among other things, led
to new and quite natural proofs for a wide range of geometric inequalities
such as the ones formulated by Brunn-Minkowski, Sobolev, Gagliardo-
Nirenberg, Beckner, Gross, Talagrand, Otto-Villani and their extensions
by many others. While this paper continues in this spirit, we however propose
here a basic framework to which all of these inequalities belong, and
a general unifying principle from which many of them follow. This basic
inequality relates the relative total energy - internal, potential and interactive
- of two arbitrary probability densities, their Wasserstein distance,
their barycentres and their entropy production functional. The framework
is remarkably encompassing as it implies many old geometric - Gaussian
and Euclidean - inequalities as well as new ones, while allowing a direct
and unified way for computing best constants and extremals. As expected,
such inequalities also lead to exponential rates of convergence to equilibria
for solutions of Fokker-Planck and McKean-Vlasov type equations. The
principle also leads to a remarkable correspondence between ground state
solutions of certain quasilinear - or semilinear - equations and stationary
solutions of nonlinear Fokker-Planck type equations. 相似文献
14.
Joseph M. Ling 《Discrete and Computational Geometry》2007,37(3):455-469
In this paper we prove four new (infinite) lists of quadratic inequalities, and four cubic inequalities, for the flag f-vectors
of 4-polytopes. These extend and supplement the only four currently known non-linear inequalities, which were proved by Bayer
in 1987. The new lists of inequalities for flag f-vectors yield new lists of inequalities for
f-vectors of 4-polytopes. Using the latter, we managed to improve an estimate discovered by Hoppner and Ziegler concerning
upper bounds of f1 in terms of f0 and f3. 相似文献
15.
Omar Hirzallah 《Linear algebra and its applications》2007,424(1):71-82
We prove several singular value inequalities and norm inequalities involving sums and direct sums of Hilbert space operators. It is shown, among other inequalities, that if X and Y are compact operators, then the singular values of are dominated by those of X ⊕ Y. Applications of these inequalities are also given. 相似文献
16.
In this paper, we establish several new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which generalize or improve all related existing ones. Then we use the Lyapunov-type inequalities obtained in this paper to derive a better lower bound for the generalized eigenvalues of the one-dimensional quasilinear elliptic system with the Dirichlet boundary conditions. 相似文献
17.
18.
Liming Wu 《Probability Theory and Related Fields》2000,118(3):427-438
By means of the martingale representation, we establish a new modified logarithmic Sobolev inequality, which covers the previous
modified logarithmic Sobolev inequalities of Bobkov-Ledoux and the L
1-logarithmic Sobolev inequality obtained in our previous work. From it we derive several sharp deviation inequalities of Talagrand's
type, by following the powerful Herbst method developed recently by Ledoux and al. Moreover this new modified logarithmic
Sobolev inequality is transported on the discontinuous path space with respect to the law of a Lévy process.
Received: 16 June 1999 / Revised version: 13 March 2000 / Published online: 12 October 2000 相似文献
19.
Qi-ming Zhang 《Journal of Difference Equations and Applications》2013,19(9):1467-1484
In this paper, we establish several new Lyapunov-type inequalities for discrete linear Hamiltonian systems when the end-points are not necessarily usual zeros, but rather, generalized zeros, which generalize and improve almost all related existing ones. Applying these inequalities, an optimal stability criterion is obtained. 相似文献
20.
In this paper, we will establish several Lyapunov inequalities for linear Hamiltonian systems, which unite and generalize the most known ones. For planar linear Hamiltonian systems, the connection between Lyapunov inequalities and estimates of eigenvalues of stationary Dirac operators will be given, and some optimal stability criterion will be proved. 相似文献