Concave function

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

Probably) Concave Graph Matching

Abstract: In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of \emph{conditionally concave} and \emph{probably conditionally concave} energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (\eg, doubly stochastic) are with high probability extreme points of the matching polytope (\eg, permutations).

Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions

Abstract: Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu (Atangana and Baleanu, 2016). In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators is proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities.

Positive Solutions for a System of Semipositone Fractional Difference Boundary Value Problems

Abstract: Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling behavior of our nonlinear terms.

Concave Generalized Flows with Applications to Market Equilibria

Abstract: We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper [Truemper K (1978) Optimal flows in nonlinear gain networks. Networks 8(1):17–36] and by Shigeno [Shigeno M (2006) Maximum network flows with concave gains. Math. Programming 107(3):439–459]. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an e-approximate solution in O(m(mσ+log n)log(MUm/e)) arithmetic operations, where M and U are upper bounds on simple parameters, and σ is the complexity of a value oracle query for the gain functions. This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg et al. [Goldberg AV, Plotkin SA, Tardos E (1991) Combinatorial algorithms for the generalized circulation problem. Math. Oper. Res. 16(2):351–381], not using any cycle cancellations. We sho...

Optimal buffer allocation in a multicell system

Abstract: Motivated by a layout design problem in the electronics industry, we study in this article the allocation of buffer space among a set of cells. Each cell processes a given part family and has its own revenue-cost structure. The objective of the optimal allocation is to maximize the net profit function (total production profits minus total buffer allocation costs). According to the flow pattern of jobs, the cells are categorized into two types. A type 1 cell is modeled as a Jackson network; a type 2 cell is modeled as an ordered-entry system with heterogeneous servers. Both models have finite waiting room, due to the buffer capacity allocated to the cells. We show that under quite general conditions, the production rate of each cell of either type is an incresing and concave function of its buffer allocation. Exploiting this property, a marginal allocation scheme efficiently solves the optimal buffer allocation problem under increasing concave production profits and convex buffer space costs.