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1.
In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent. 相似文献
2.
In generalized fractional programming, one seeks to minimize the maximum of a finite number of ratios. Such programs are, in general, nonconvex and consequently are difficult to solve. Here, we consider a particular case in which the ratio is the quotient of a quadratic form and a positive concave function. The dual of such a problem is constructed and a numerical example is given. 相似文献
3.
On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory 总被引:1,自引:0,他引:1
J. B. G. Frenk P. Kas G. Kassay 《Journal of Optimization Theory and Applications》2007,132(3):423-439
In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming
duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions
have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions
for strong duality for a general class of optimization problems.
The authors like to thank the comments of the anonymous referees for their remarks, which greatly improved the presentation
of this paper. 相似文献
4.
5.
Lagrangian Duality and Cone Convexlike Functions 总被引:1,自引:0,他引:1
In this paper, we consider first the most important classes of cone convexlike vector-valued functions and give a dual characterization
for some of these classes. It turns out that these characterizations are strongly related to the closely convexlike and Ky
Fan convex bifunctions occurring within minimax problems. Applying the Lagrangian perturbation approach, we show that some
of these classes of cone convexlike vector-valued functions show up naturally in verifying strong Lagrangian duality for finite-dimensional
optimization problems. This is achieved by extending classical convexity results for biconjugate functions to the class of
so-called almost convex functions. In particular, for a general class of finite-dimensional optimization problems, strong
Lagrangian duality holds if some vector-valued function related to this optimization problem is closely K-convexlike and satisfies some additional regularity assumptions. For K a full-dimensional convex cone, it turns out that the conditions for strong Lagrangian duality simplify. Finally, we compare
the results obtained by the Lagrangian perturbation approach worked out in this paper with the results achieved by the so-called
image space approach initiated by Giannessi. 相似文献
6.
J. B. G. Frenk J. Gromicho S. Zhang 《Journal of Optimization Theory and Applications》1996,89(1):65-87
This paper studies the problem of deciding whether the present iteration point of some algorithm applied to a planar singlefacility min-max location problem, with distances measured by either anl
p
-norm or a polyhedral gauge, is optimal or not. It turns out that this problem is equivalent to the decision problem of whether 0 belongs to the convex hull of either a finite number of points in the plane or a finite number of differentl
q
-circles
. Although both membership problems are theoretically solvable in polynomial time, the last problem is more difficult to solve in practice than the first one. Moreover, the second problem is solvable only in the weak sense, i.e., up to a predetermined accuracy. Unfortunately, these polynomial-time algorithms are not practical. Although this is a negative result, it is possible to construct an efficient and extremely simple linear-time algorithm to solve the first problem. Moreover, this paper describes an implementable procedure to reduce the second decision problem to the first with any desired precision. Finally, in the last section, some computational results for these algorithms are reported.The work of the second author was supported by JNICT (Portugal), under Contract BD/631/90-RM, during his stay at Erasmus University in Rotterdam.The authors would like to express their acknowledgments to Jan Brinkhuis for his suggestions and support and to Joe Mitchell for suggesting the simplifications leading to Algorithm 3.1. Also, the anonymous referees are acknowledged for their careful reading of the paper and their useful comments. 相似文献
7.
Elgarøy Ø Lahav O Percival WJ Peacock JA Madgwick DS Bridle SL Baugh CM Baldry IK Bland-Hawthorn J Bridges T Cannon R Cole S Colless M Collins C Couch W Dalton G De Propris R Driver SP Efstathiou GP Ellis RS Frenk CS Glazebrook K Jackson C Lewis I Lumsden S Maddox S Norberg P Peterson BA Sutherland W Taylor K 《Physical review letters》2002,89(6):061301
We constrain f(nu) identical with Omega(nu)/Omega(m), the fractional contribution of neutrinos to the total mass density in the Universe, by comparing the power spectrum of fluctuations derived from the 2 Degree Field Galaxy Redshift Survey with power spectra for models with four components: baryons, cold dark matter, massive neutrinos, and a cosmological constant. Adding constraints from independent cosmological probes we find f(nu)<0.13 (at 95% confidence) for a prior of 0.1相似文献
8.
Frenk Hans Dekker Rommert Kleijn Marcel 《Mathematical Methods of Operations Research》1997,45(3):437-454
In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented. 相似文献
9.
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.Author on leave from D.E.I.O. (Universidade de Lisboa, Portugal). This research was supported by J.N.I.C.T. (Portugal) under contract number BD/631/90-RM. 相似文献
10.
In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known minimax
theorem of Sion. Although this proof technique was initiated by Joó and based on the intersection of upper level sets and
a clever use of the topological notion of connectedness, it is not very well known and accessible for researchers in optimization.
At the same time we simplify the original proof of Joó and give a more elementary proof of the celebrated minimax theorem
of Sion. 相似文献