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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.


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TL;DR: A procedure for globally minimizing a concave function over a bounded polytope by successively minimizing the function over polytopes containing the feasible region, and collapsing to the feasibleregion is presented.
Abstract: We present a procedure for globally minimizing a concave function over a bounded polytope by successively minimizing the function over polytopes containing the feasible region, and collapsing to the feasible region. The initial containing polytope is a simplex, and, at the kth iteration, the procedure chooses the most promising vertex of the current containing polytope to refine the approximation. The method generates a tree whose ultimate terminal nodes coincide with the vertices of the feasible region, and accounts for the vertices of the containing polytopes.

37 citations

Journal ArticleDOI
TL;DR: The main result proved is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain.
Abstract: The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of this result and a few applications to mathematical programming are also considered.

37 citations

Journal ArticleDOI
TL;DR: In this article, the authors prove that the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics is convex and the dominant eigenvalue (λ 1) of any projection 2 × 2 matrix to be either convex, or concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates).

37 citations

Journal ArticleDOI
TL;DR: In this article, the authors define temporal convexity and concavity for continuous time stochastic processes and apply it to reliability theory, queueing theory, branching processes and record values.

37 citations

Journal ArticleDOI
TL;DR: This paper showed that the Renyi entropy of general probability densities solving the nonlinear diffusion of order p is a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source-type solutions.
Abstract: We associate to the p-th Renyi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in $R^n$. We show that the Renyi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source-type solutions. We then shown that the p-th Renyi entropy power of a probability density which solves the nonlinear diffusion of order p, is a concave function of time. This result extends Costa's concavity inequality for Shannon's entropy power to Renyi entropies.

37 citations


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