scispace - formally typeset
Search or ask a question
Topic

Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: The article describes the details of how the main idea of transformed density rejection can be used to construct algorithm TDRMV that generates random tuples from a multivariate log-concave distribution with a computable density.
Abstract: Different universal methods (also called automatic or black-box methods) have been suggested for sampling form univariate log-concave distributions. The descriptioon of a suitable universal generator for multivariate distributions in arbitrary dimensions has not been published up to now. The new algorithm is based on the method of transformed density rejection. To construct a hat function for the rejection algorithm the multivariate density is transformed by a proper transformation T into a concave function (in the case of log-concave density T(x) = log(x).) Then it is possible to construct a dominating function by taking the minimum of serveral tangent hyperplanes that are transformed back by T-1 into the original scale. The domains of different pieces of the hat function are polyhedra in the multivariate case. Although this method can be shown to work, it is too slow and complicated in higher dimensions. In this article we split the ℝn into simple cones. The hat function is constructed piecewise on each of the cones by tangent hyperplanes. The resulting function is no longer continuous and the rejection constant is bounded from below but the setup and the generation remains quite fast in higher dimensions; for example, n = 8. The article describes the details of how this main idea can be used to construct algorithm TDRMV that generates random tuples from a multivariate log-concave distribution with a computable density. Although the developed algorithm is not a real black box method it is adjustable for a large class of log-concave densities.

35 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one-to-one correspondence between three classes of existing spatial agglomeration models, here designated as spatialaccessibility models, endogenous-contact models, and fixed-contact model, which not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model.
Abstract: A wide variety of existing models of spatial agglomeration postulate additive-interaction effects among agents. In this paper, a synthesis of such models is achieved by establishing certain mathematical equivalences between them. In particular, it is shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one-to-one correspondence between three classes of existing models, here designated as spatial-accessibility models, endogenous-contact models, and fixed-contact models. These correspondences not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model. A series of examples are drawn from the literature to illustrate these results.

35 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered a variant of bin packing called bin packing with general cost structures (GCBP) and designed an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem.
Abstract: Following the work of Anily et al., we consider a variant of bin packing called bin packing with general cost structures (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However, in GCBP, the cost of a bin is not 1 as in classic bin packing, but it is a non-decreasing and concave function of the number of items packed in it, where the cost of an empty bin is zero. The construction of the AFPTAS requires novel techniques for dealing with small items, which are developed in this work. In addition, we develop a fast approximation algorithm which acts identically for all non-decreasing and concave functions, and has an asymptotic approximation ratio of 1.5 for all functions simultaneously.

35 citations

Posted Content
TL;DR: In this paper, the Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals have been defined and a new identity for fractional integral integrals has been defined.
Abstract: New identity for fractional integrals have been defined. By using of this identity, some new Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral have been developed. Our results have some relationships with the result of Avci et al., proved in AKO.

34 citations

Journal ArticleDOI
TL;DR: It is shown that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution.
Abstract: We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called ``Uniformity Principle'' of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.

34 citations


Network Information
Related Topics (5)
Markov chain
51.9K papers, 1.3M citations
74% related
Bounded function
77.2K papers, 1.3M citations
74% related
Polynomial
52.6K papers, 853.1K citations
72% related
Upper and lower bounds
56.9K papers, 1.1M citations
72% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
72% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202240
202158
202049
201952
201860