scholarly journals A minimization algorithm for limit extremal problems on convex compactum

2019 ◽  
Author(s):  
Özkan Deǧer
Keyword(s):  
Extremal Problems ◽  
Minimization Algorithm ◽  
Convex Compactum

Sum-Rate Optimization Constrained by Consumed Power for Multi- Antenna Non-Regenerative Relay Network

2020 ◽  
Vol 10 (2) ◽  
pp. 143-152 ◽  
Author(s):  
Maryam Alibeigi ◽  
Shahriar S. Moghaddam
Keyword(s):  
Relay Network ◽  
Minimization Algorithm ◽  
Amplify And Forward ◽  
Relay Nodes ◽  
Convex Problem ◽  
Semidefinite Programming Problem ◽  
Total Leakage ◽  
Sum Rate ◽  
Rate Optimization ◽  
Novel Algorithm

Background & Objective: This paper considers a multi-pair wireless network, which communicates peer-to-peer using some multi-antenna amplify-and-forward relays. Maximizing the throughput supposing that the total relay nodes’ power consumption is constrained, is the main objective of this investigation. We prove that finding the beamforming matrix is not a convex problem. Methods: Therefore, by using a semidefinite relaxation technique we find a semidefinite programming problem. Moreover, we propose a novel algorithm for maximizing the total signal to the total leakage ratio. Numerical analyses show the effectiveness of the proposed algorithm which offers higher throughput compared to the existing total leakage minimization algorithm, with much less complexity. Results and Conclusion: Furthermore, the effect of different parameters such as, the number of relays, the number of antennas in each relay, the number of transmitter/receiver pairs and uplink and downlink channel gains are investigated.

scholarly journals Clipped Matrix Completion: A Remedy for Ceiling Effects

2019 ◽  
Vol 33 ◽  
pp. 5151-5158
Author(s):  
Takeshi Teshima ◽  
Miao Xu ◽  
Issei Sato ◽  
Masashi Sugiyama
Keyword(s):  
Matrix Completion ◽  
Low Rank ◽  
Trace Norm ◽  
Minimization Algorithm ◽  
Benchmark Data ◽  
Hinge Loss ◽  
Norm Minimization ◽  
Rank Matrix ◽  
Recovery Error ◽  
Low Rank Matrix

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a low-rank matrix from various information deficits by using the principle of low-rank completion. However, the current theoretical guarantees for low-rank MC do not apply to clipped matrices, as the deficit depends on the underlying values. Therefore, the feasibility of clipped matrix completion (CMC) is not trivial. In this paper, we first provide a theoretical guarantee for the exact recovery of CMC by using a trace-norm minimization algorithm. Furthermore, we propose practical CMC algorithms by extending ordinary MC methods. Our extension is to use the squared hinge loss in place of the squared loss for reducing the penalty of overestimation on clipped entries. We also propose a novel regularization term tailored for CMC. It is a combination of two trace-norm terms, and we theoretically bound the recovery error under the regularization. We demonstrate the effectiveness of the proposed methods through experiments using both synthetic and benchmark data for recommendation systems.

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