Topic
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: This paper investigates the energy-efficient power control for device-to-device (D2D) communications underlaying cellular networks, where uplink resource blocks allocated to one cellular user equipment are reused by multiple D2D pairs and co-channel interference caused by resource sharing becomes a significant challenge.
Abstract: In this paper, we investigate the energy-efficient power control for device-to-device (D2D) communications underlaying cellular networks, where uplink resource blocks allocated to one cellular user equipment are reused by multiple D2D pairs and co-channel interference caused by resource sharing becomes a significant challenge. We consider both the total energy efficiency (EE) and individual EE optimization problems, which are fractional programming and generalized fractional programming problems, respectively, and are hard to tackle due to their non-concave nature. We first transform them into equivalent optimization problems in parametric subtractive forms, which fit in a class of non-concave optimization methods known as difference of two concave functions programming, and then solve them using Dinkelbach and branch-and-bound methods to give global optimal solutions. Due to the unaffordable complexity of the global optimal solution, we further propose sub-optimal schemes through adding constraints on the interferences to convert the non-concave problems into concave ones and to give sub-optimal solutions with reasonable complexity. The sub-optimal solution gives a tight lower bound on the optimal EE. Simulation results are presented to demonstrate the effectiveness of the proposed schemes.
118 citations
TL;DR: Two new algorithms for maximizing a separable concave function on a polymatroid are presented, and it is shown that the Decomposition Algorithm runs in polynomial time (in the discrete version) for network and generalized symmetric polymatroids.
115 citations
TL;DR: In this paper, an approach using Lagrangian method to solve the optimal chiller loading (OCL) problem and to improve the deficiencies of conventional methods is presented, where the coefficient of performance (COP) of a chiller is chosen as the objective function for the reason of being a concave function.
114 citations
01 Jan 1996
TL;DR: The proposed concave minimization formulation, a successive linearization algorithm without stepsize terminates after a maximum average of 7 linear programs on problems with as many as 4192 points in 14-dimensional space, is quite effective and more efficient than other approaches.
Abstract: Two fundamental problems of machine learning, misclassification minimization [10, 24, 18] and feature selection, [25, 29, 14] are formulated as the minimization of a concave function on a polyhedral set. Other formulations of these problems utilize linear programs with equilibrium constraints [18, 1, 4, 3] which are generally intractable. In contrast, for the proposed concave minimization formulation, a successive linearization algorithm without stepsize terminates after a maximum average of 7 linear programs on problems with as many as 4192 points in 14-dimensional space. The algorithm terminates at a stationary point or a global solution to the problem. Preliminary numerical results indicate that the proposed approach is quite effective and more efficient than other approaches.
114 citations
TL;DR: In this article, the authors established the limiting distribution of the resulting estimator of the mode M(f0) and established a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.
Abstract: We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form f0=exp ϕ0 where ϕ0 is a concave function on ℝ. The pointwise limiting distributions depend on the second and third derivatives at 0 of Hk, the “lower invelope” of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of ϕ0=log f0 at the point of interest. We also establish the limiting distribution of the resulting estimator of the mode M(f0) and establish a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.
113 citations