Generalized Concavity

Avriel, Mordecai; Diewert, W. Erwin; Schaible, Siegfried; Zang, Israël

doi:10.1137/1.9780898719437

Cited by 94 publications

(71 citation statements)

References 0 publications

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“…Indeed, the second constraint of problem (14) involves the ratio of a convex function over a concave function. Since both functions at numerator and denumerator of (13) are differentiable and positive for all p satisfying the first and third constraint of problem (14), the function is pseudo-convex [23], and all its sub-level sets are convex sets. This argument, coupled with the convexity of the objective function and of the sets defined by the first and third constraints, proves the convexity of the problem (14), whose global solution can be found using efficient numerical tools [24].…”

Section: A Minimum Sampling Rate With Learning Constraintsmentioning

confidence: 99%

“…Problem (16) is a convex/concave fractional program [25], i.e., a problem that involves the minimization of the ratio of a convex function over a concave function, both defined over the convex set C. In particular, as mentioned before, the objective function of (16) is pseudo-convex in C [23]. As a consequence, any local minimum of problem (16) is also a global minimum [25].…”

Section: B Minimum Msd With Sampling and Learning Constraintsmentioning

confidence: 99%

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Optimal sampling strategies for adaptive learning of graph signals

Lorenzo

Banelli

Barbarossa

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-The aim of this paper is to propose optimal sampling strategies for adaptive learning of signals defined over graphs. Introducing a novel least mean square (LMS) estimation strategy with probabilistic sampling, we propose two different methods to select the sampling probability at each node, with the aim of optimizing the sampling rate, or the mean-square performance, while at the same time guaranteeing a prescribed learning rate. The resulting solutions naturally lead to sparse sampling probability vectors that optimize the tradeoff between graph sampling rate, steady-state performance, and learning rate of the LMS algorithm. Numerical simulations validate the proposed approach, and assess the performance of the proposed sampling strategies for adaptive learning of graph signals.

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Section: A Minimum Sampling Rate With Learning Constraintsmentioning

confidence: 99%

Section: B Minimum Msd With Sampling and Learning Constraintsmentioning

confidence: 99%

Optimal sampling strategies for adaptive learning of graph signals

Lorenzo

Banelli

Barbarossa

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…Since the numerator of the objective function is positive and concave and the denominator is positive and convex (affine), (15) belongs to a class of optimization problems called concave fractional programs [19]. Furthermore, a concave fractional program with an affine denominator can be transformed into a concave program using a transformation proposed by Charnes and Cooper [19].…”

Section: Power Allocationmentioning

confidence: 99%

“…Furthermore, a concave fractional program with an affine denominator can be transformed into a concave program using a transformation proposed by Charnes and Cooper [19].…”

Section: Power Allocationmentioning

confidence: 99%

Energy-Efficient Frequency and Power Allocation for Cognitive Radios in Television Systems

Illanko

Naeem

Anpalagan

et al. 2016

IEEE Systems Journal

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Energy-efficient resource allocation for cognitive radios operating in television systems (TV white spaces) presents a unique challenge compared with other cognitive radios because the interference constraint is for the whole frequency band rather than per carrier. This paper presents a subchannel and power allocation protocol that maximizes the energy efficiency (EE) of transmissions from a cognitive base station operating in the TV white spaces. The system model conforms to the IEEE 802.22 standard, and the proposed two-step solution to the EE maximization problem satisfies users' minimum rate requirements and keeps the interference to the primary users in the neighboring areas below a specified threshold. The first step of the protocol is a near-optimal but low-complexity subchannel assignment. This is followed by an optimal power allocation procedure that is obtained by analyzing the Karush-Kuhn-Tucker conditions. The computational complexity of the resulting resource allocation protocol is the same as that of the least complex resource allocation protocol for orthogonal frequency division multiple access (OFDMA) downlinks in the literature. Simulation results show that our protocol achieves higher EE compared with a modified and improved version of the OFDMA protocol from the literature.

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“…Progresses in multi-ratio fractional optimization have led to efficient global optimization algorithms for the problem of maximizing the smallest of several ratios, and to effective algorithms for maximizing or minimizing a sum-of-ratios [2]. The former problem is considerably more tractable than the later, as many of the properties of concave-convex single-ratio problems, such as the semistrictly quasiconcavity of its objective function [3], are inherited by the problem of maximizing the smallest concave-convex ratio.…”

Section: Introductionmentioning

confidence: 99%