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1.
In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the ε-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for
properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses
by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables.
We prove results on (weakly, properly) efficient solutions. The improved ε-constraint method that we propose combines both modifications.
The research of M. Ehrgott was partially supported by University of Auckland Grant 3602178/9275 and by Deutsche Forschungsgemeinschaft
Grant Ka 477/27-1.
The research of S. Ruzika was partially supported by Deutsche Forschungsgemeinschaft Grant HA 1795/7-2.
The authors thank the anonymous referees, whose comments helped improving the presentation of the paper including a shorter
proof of Theorem 3.1. 相似文献
2.
S. J. Dilworth E. Odell T. Schlumprecht A. Zsák 《Foundations of Computational Mathematics》2008,8(6):703-736
Let (e
i
) be a dictionary for a separable infinite-dimensional Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn
usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach
space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c
0. We also show that, for every ε>0, the unit ball of every separable infinite-dimensional Banach space X contains a dictionary (x
i
) such that the additive group generated by (x
i
) is (3+ε)−1-separated and 1/3-dense in X.
相似文献
3.
The paper deals with the notions of weak stability and weak generalized convolution with respect to a generalized convolution, introduced by Kucharczak and Urbanik. We study properties of such objects and give examples of weakly stable measures with respect to the Kendall convolution. Moreover, we show that in the context of non-commutative probability, two operations: the q-convolution and the (q,1)-convolution satisfy the Urbanik??s conditions for a generalized convolution, interpreted on the set of moment sequences. The weak stability reveals the relation between two operations. 相似文献
4.
Á. Császár 《Acta Mathematica Hungarica》2008,121(4):395-400
It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following
the paper [3], we discuss some questions related to this construction.
Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786. 相似文献
5.
Olcay Arslan 《Journal of multivariate analysis》2004,89(2):420-337
In this paper, we introduce a new family of multivariate distributions as the scale mixture of the multivariate power exponential distribution introduced by Gómez et al. (Comm. Statist. Theory Methods 27(3) (1998) 589) and the inverse generalized gamma distribution. Since the resulting family includes the multivariate t distribution and the multivariate generalization of the univariate GT distribution introduced by McDonald and Newey (Econometric Theory 18 (11) (1988) 4039) we call this family as the “multivariate generalized t-distributions family”, or MGT for short. We show that this family of distributions belongs to the elliptically contoured distributions family, and investigate the properties. We give the stochastic representation of a random variable distributed as a multivariate generalized t distribution. We give the marginal distribution, the conditional distribution and the distribution of the quadratic forms. We also investigate the other properties, such as, asymmetry, kurtosis and the characteristic function. 相似文献
6.
Á. Császár 《Acta Mathematica Hungarica》2008,120(4):351-354
The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is
replaced by a generalized topology.
Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786. 相似文献
7.
Jing Ping YANG Shi Hong CHENG Xiao Qian WANG 《数学学报(英文版)》2007,23(3):467-478
This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 (a, b) family, bivariate recursive equations for the joint distribution of the cedent's aggregate claims and the reinsurer's aggregate claims are obtained. 相似文献
8.
In this paper, the hybrid steepest descent methods are extended to develop new iterative schemes for finding the zeros of
bounded, demicontinuous and φ-strongly accretive mappings in uniformly smooth Banach spaces. Two iterative schemes are proposed. Strong convergence results
are established and applications to variational inequalities are given.
In this research, the first author was partially supported by the National Science Foundation of China (10771141), Ph.D. Program
Foundation of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality
(075105118). The third author was partially supported by Grant NSC 96-2628-E-110-014-MY3. 相似文献
9.
Vyacheslav M. Abramov 《Queueing Systems》2008,59(1):63-86
In this paper continuity theorems are established for the number of losses during a busy period of the M/M/1/n queue. We consider an M/GI/1/n queueing system where the service time probability distribution, slightly different in a certain sense from the exponential
distribution, is approximated by that exponential distribution. Continuity theorems are obtained in the form of one or two-sided
stochastic inequalities. The paper shows how the bounds of these inequalities are changed if further assumptions, associated
with specific properties of the service time distribution (precisely described in the paper), are made. Specifically, some
parametric families of service time distributions are discussed, and the paper establishes uniform estimates (given for all
possible values of the parameter) and local estimates (where the parameter is fixed and takes only the given value). The analysis
of the paper is based on the level crossing approach and some characterization properties of the exponential distribution.
Dedicated to Vladimir Mikhailovich Zolotarev, Victor Makarovich Kruglov, and to the memory of Vladimir Vyacheslavovich Kalashnikov. 相似文献
10.
A new series representation of the exact distribution of Hotelling's generalized T02 statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1], 215–225), which are convergent on the interval [0, 1), are also derived quite simply from our formulae. The paper therefore provides a solution to the long standing problem of the exact distribution of the T02 statistic in the general case. 相似文献
11.
Josefina Alvarez Martha Guzmn-Partida 《Journal of Mathematical Analysis and Applications》2002,270(2):235-434
We characterize those tempered distributions which are S′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean case and the product domain case. In the Euclidean case, we consider a class of kernels that includes Riesz kernels, Calderón–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hörmander multipliers. In the product domain case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n-dimensional Hilbert kernel. 相似文献
12.
Tadeusz Gerstenkorn 《Central European Journal of Mathematics》2004,2(4):527-537
This paper presents a compound of the generalized negative binomial distribution with the generalized beta distribution.
In the introductory part of the paper, we provide a chronological overview of recent developments in the compounding of distributions,
including the Polish results. Then, in addition to presenting the probability function of the compound generalized negative
binomial-generalized beta distribution, we present special cases as well as factorial and crude moments of some compound distributions. 相似文献
13.
14.
W. K. Min 《Acta Mathematica Hungarica》2008,121(3):283-292
We introduce and study the concepts of weak neighborhood systems, weak neighborhood spaces, ω(ψ, ψ′)-continuity, ω-continuity and ω*-continuity on WNS’s.
This work was supported by a grant from Research Institute for Basic Science at Kangwon National University. 相似文献
15.
Let F(x) be a distribution function supported on [0, ∞) with an equilibrium distribution function F
e
(x). In this paper we pay special attention to the hazard rate function r
e
(x) of F
e
(x), which is also called the equilibrium hazard rate (E.H.R.) of F(x). By the asymptotic behavior of r
e
(x) we give a criterion to identify F(x) to be heavy-tailed or light-tailed. Moreover, we introduce two subclasses of heavy-tailed distributions, i.e., ℳ and ℳ*, where ℳ contains almost all the most important heavy-tailed distributions in the literature. Some further discussions on the closure
properties of ℳ and ℳ* under convolution are given, showing that both of them are ideal heavy-tailed subclasses. In the paper we also study the
model of independent difference ξ = Z − θ, where Z and θ are two independent and non-negative random variables. We give intimate relationships of the tail distributions of ξ and Z, as well as relationships of tails of their corresponding equilibrium distributions. As applications, we apply the properties
of class ℳ to risk theory. In the final, some miscellaneous problems and examples are laid, showing the complexity of characterizations
on heavy-tailed distributions by means of r
e
(x).
相似文献
16.
In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The
concept of η-bonvexity/generalized η-bonvexity is adopted in order to discuss weak, strong and strict converse duality theorems.
The research of Z. Husain is supported by the Department of Atomic Energy, Government of India, under the NBHM Post-Doctoral
Fellowship Program No. 40/9/2005-R&D II/1739. 相似文献
17.
In this paper, we assume that the data are distributed according to a binomial distribution whose probabilities follow a generalized
linear model. To fit the data the minimum φ-divergence estimator is studied as a generalization of the maximum likelihood estimator. We use the minimum φ-divergence estimator, which is the basis of some new statistics, for solving the problems of testing in a generalized linear
model with binary data. A wide simulation study is carried out for studying the behavior of the new family of estimators as
well as of the new family of test statistics.
This work was partially supported by Grant MTM2006-06872 and UCM2006-910707. 相似文献
18.
Eugenia Cheng 《Applied Categorical Structures》2007,15(4):439-453
We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.
相似文献
19.
In this paper, we investigate the problem of robust H
∞ control for singular systems with polytopic time-varying parameter uncertainties. By introducing the notion of generalized
quadratic H
∞ performance, the relationship between the existence of a robust H
∞ dynamic state feedback controller and that of a robust H
∞ static state feedback controller is given. By using matrix inequalities, the existence conditions of robust H
∞ static state feedback and dynamic output feedback controllers are derived. Moreover, the design methods for such controllers
are provided in terms of the solutions of matrix inequalities. An example is also presented to demonstrate the validity of
the proposed methods.
__________
Translated from Journal of Northeastern University (Natural Science), 2004, 25(2): 110–113 相似文献
20.
A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable.
The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China. 相似文献