Complementary Geometric Programming

Avriel, Mordecai; Williams, Adrian

doi:10.1137/0119011

Cited by 183 publications

(70 citation statements)

References 6 publications

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“…First, the ratio-of-posynomial constraints can be replaced by posynomial constraints using the single condensation method [19]. Specifically, consider a constraint…”

Section: Sequential Gp-based Solutionmentioning

confidence: 99%

Admission and power control for cognitive radio networks by sequential geometric programming

Dall’Anese

Kim

Giannakis

2011

2011 17th International Conference on Digital Signal Processing (DSP)

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In cognitive radio (CR) networks, power control is an effective means to limit the interference caused by the CRs upon the incumbent primary users (PUs) to ensure cohabitation of the two systems. When all CR links can not be active at the same time due to excessive interference, an admission control mechanism is necessary to schedule the CR links. Key to both tasks is accurate knowledge of the CR-to-PU channel gains. However, CRs generally face difficulties in estimating the channel gains very accurately, often due to lack of explicit support from the PU systems. In this work, admission and power control algorithms are developed to account for channel uncertainty through probabilistic interference constraints. Both log-normal shadowing and small-scale fading effects are considered through suitable approximations. The resulting problems can be solved via sequential geometric programming. The admission control is based on solving feasibility problems, whereby CR links violating the interference constraints the most are dropped progressively. The feasible point thus found to initialize the power control iterative solver.

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“…First, the ratio-of-posynomial constraints can be replaced by posynomial constraints using the single condensation method [19]. Specifically, consider a constraint…”

Section: Sequential Gp-based Solutionmentioning

confidence: 99%

Admission and power control for cognitive radio networks by sequential geometric programming

Dall’Anese

Kim

Giannakis

2011

2011 17th International Conference on Digital Signal Processing (DSP)

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“…Problem 2 was studied in an abstract setting by Singer [17], and from a computational point of view by the authors of the present paper [23]. Prior to the mentioned works, problems with reverse convex constraints were also studied by Rosen [16], Avriel [1], Avriel and Williams [2], [3], and Meyer [11], though most of these authors either concentrated on some theoretical aspects of the problem or were concerned mainly with finding KuhnTucker points or local minima. Problems of type 3 were discussed in Ueing [33], Tuy [26], [29], Thach [18], and also Thoai [22].…”

Section: Introductionmentioning

confidence: 95%

On the global minimization of a convex function under general nonconvex constraints

Tụy

Thường

1988

Appl Math Optim

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“…For this transformation, we apply the complementary geometric programming (CGP) and variable relaxation to convert (6) into the geometric programming (GP) formulation. We refer the interested readers for the background of CGP to [19]- [21]. For (7), we apply the relaxation technique to convert binary variables into continuous ones.…”

Section: Proposed Algorithmmentioning

confidence: 99%