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Concave function

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


Papers
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Journal ArticleDOI
TL;DR: In this paper, different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies have been proved, and the equality cases in all these inequalities have been characterized.

43 citations

Book ChapterDOI
01 Jul 1993
TL;DR: In this paper, the authors presented a technique which enabled them to solve the parametric minimum cycle problem with a xed number of parameters in strongly polynomial time in a convex set given as an intersection of k halfspaces.
Abstract: In the authors introduced a technique which enabled them to solve the parametric minimum cycle problem with a xed number of parameters in strongly polynomial time In the current paper we present this technique as a general tool In order to allow for an independent reading of this paper we repeat some of the de nitions and propositions given in Some proofs are not repeated however and instead we supply the interested reader with appropriate pointers Suppose Q R is a convex set given as an intersection of k halfspaces and let g Q R be a concave function that is computable by a piecewise a ne algo rithm i e roughly an algorithm that performs only multiplications by scalars additions and comparisons of intermediate values which depend on the input Assume that such an algorithm A is given and the maximal number of op erations required by A on any input i e point in Q is T We show that under these assumptions for any xed d the function g can be maximized in a number of operations polynomial in k and T We also present a general frame work for parametric extensions of problems where this technique can be used to obtain strongly polynomial algorithms Norton Plotkin and Tardos applied a similar scheme and presented additional applications

43 citations

Journal ArticleDOI
07 Oct 2005
TL;DR: In this article, it was shown that the trace norm of a nonnegative concave function on n×n matrices is a unitarily invariant norm, where the norm is defined by
Abstract: Let f(t) be a nonnegative concave function on 0 < t < ∞ with f(0) = 0, and let X, Y be n×n matrices. Then it is known that ||f(|X+Y|)|| 1 ≤ ||f(|X|)|| 1 + ||f(|Y|)|| 1 , where ||·|| 1 is the trace norm. We extend this result to all unitarily invariant norms and prove some inequalities of eigenvalue sums.

42 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider a planner choosing treatments for observationally identical persons who vary in their response to treatment, and assume that the objective is to maximize a concave-monotone function f( ·) of the success rate and show that admissibility depends on the curvature of f ( ·).

42 citations

Posted Content
TL;DR: In this paper, the authors argue that the relevant assumption for the convexity property to hold is the implicit assumption about the choice variable in the representative firm's maximisation problem.
Abstract: Hartman (1972) and Abel (1983) showed that when firms are competitive and there is flexibility of labour relative to capital, marginal profitability of capital is a convex function of the stochastic variable (e.g., price); by Jensen’s inequality, this means that uncertainty increases the expected profitability of capital, which increases the incentive to invest. We argue that, besides factor substitutability, the relevant assumption for the convexity property to hold is the implicit assumption about the choice variable in the representative firm’s maximisation problem: the assumption of perfect competition implies that the choice variable is output and that price is exogenous. However, in the case of a firm facing a downward-sloping demand curve, both output and output price emerge as the possible choice variable. We show that, when price is the choice variable, marginal profitability of capital is a concave function of the stochastic variable; hence, by Jensen’s inequality, an increase in uncertainty decreases the expected profitability of capital. We also show that keeping the assumption of factor substitutability but changing the share of labour in the production function has an important impact on the degree of concavity/convexity of the capital profit function.

41 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202240
202158
202049
201952
201860