A concave–convex problem with a variable operator

2017 ◽  
Vol 57 (1) ◽  
Author(s):  
Alexis Molino ◽  
Julio D. Rossi
Keyword(s):  
Variable Operator ◽  
Convex Problem

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 Physical layer security transmission scheme based on artificial noise in cooperative SWIPT NOMA system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yong Jin ◽  
Zhentao Hu ◽  
Dongdong Xie ◽  
Guodong Wu ◽  
Lin Zhou
Keyword(s):  
Interference Cancellation ◽  
Physical Layer Security ◽  
High Energy ◽  
Physical Layer ◽  
Base Station ◽  
Artificial Noise ◽  
Transmitted Power ◽  
Transmission Scheme ◽  
Convex Problem ◽  
Security Problem

AbstractAiming at high energy consumption and information security problem in the simultaneous wireless information and power transfer (SWIPT) multi-user wiretap network, we propose a user-aided cooperative non-orthogonal multiple access (NOMA) physical layer security transmission scheme to minimize base station (BS) transmitted power in this paper. In this scheme, the user near from BS is adopted as a friendly relay to improve performance of user far from BS. An energy harvesting (EH) technology-based SWIPT is employed at the near user to collect energy which can be used at cooperative stage. Since eavesdropper in the downlink of NOMA system may use successive interference cancellation (SIC) technology to obtain the secrecy information of receiver, to tackle this problem, artificial noise (AN) is used at the BS to enhance security performance of secrecy information. Moreover, semidefinite relaxation (SDR) method and successive convex approximation (SCA) technique are combined to solve the above non-convex problem. Simulation results show that in comparison with other methods, our method can effectively reduce the transmitted power of the BS on the constraints of a certain level of the secrecy rates of two users.

scholarly journals Joint optimization of computing ratio and access points’ density for mixed mobile edge/cloud computing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tianqi Jing ◽  
Shiwen He ◽  
Fei Yu ◽  
Yongming Huang ◽  
Luxi Yang ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Coverage Probability ◽  
Optimization Problem ◽  
Mobile Cloud Computing ◽  
Low Complexity ◽  
Mixed Integer ◽  
Joint Optimization ◽  
Mobile Cloud ◽  
Convex Problem

AbstractCooperation between the mobile edge computing (MEC) and the mobile cloud computing (MCC) in offloading computing could improve quality of service (QoS) of user equipments (UEs) with computation-intensive tasks. In this paper, in order to minimize the expect charge, we focus on the problem of how to offload the computation-intensive task from the resource-scarce UE to access point’s (AP) and the cloud, and the density allocation of APs’ at mobile edge. We consider three offloading computing modes and focus on the coverage probability of each mode and corresponding ergodic rates. The resulting optimization problem is a mixed-integer and non-convex problem in the objective function and constraints. We propose a low-complexity suboptimal algorithm called Iteration of Convex Optimization and Nonlinear Programming (ICONP) to solve it. Numerical results verify the better performance of our proposed algorithm. Optimal computing ratios and APs’ density allocation contribute to the charge saving.

scholarly journals SOCP Relaxations of Optimal Power Flow Problem Considering Current Margins in Radial Networks

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 3164 ◽  
Author(s):  
Yuwei Chen ◽  
Ji Xiang ◽  
Yanjun Li
Keyword(s):  
Power Systems ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Additional Term ◽  
Transmission Losses ◽  
Stability Margins ◽  
Optimal Power ◽  
Second Order Cone ◽  
Convex Problem ◽  
Generation Costs

Optimal power flow (OPF) is a non-linear and non-convex problem that seeks the optimization of a power system operation point to minimize the total generation costs or transmission losses. This study proposes an OPF model considering current margins in radial networks. The objective function of this OPF model has an additional term of current margins of the line besides the traditional transmission losses and generations costs, which contributes to thermal stability margins of power systems. The model is a reformulated bus injection model with clear physical meanings. Second order cone program (SOCP) relaxations for the proposed OPF are made, followed by the over-satisfaction condition guaranteeing the exactness of the SOCP relaxations. A simple 6-node case and several IEEE benchmark systems are studied to illustrate the efficiency of the developed results.

scholarly journals Bounded solutions of a difference equation with finite number of jumps of operator coefficient

2020 ◽  
Vol 12 (1) ◽  
pp. 165-172
Author(s):  
A. Chaikovs'kyi ◽  
O. Lagoda
Keyword(s):  
Difference Equation ◽  
Finite Number ◽  
Existence And Uniqueness ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Operator Coefficient ◽  
Bounded Solutions ◽  
Piecewise Constant ◽  
Variable Operator ◽  
Necessary And Sufficient

We study the problem of existence of a unique bounded solution of a difference equation with variable operator coefficient in a Banach space. There is well known theory of such equations with constant coefficient. In that case the problem is solved in terms of spectrum of the operator coefficient. For the case of variable operator coefficient correspondent conditions are known too. But it is too hard to check the conditions for particular equations. So, it is very important to give an answer for the problem for those particular cases of variable coefficient, when correspondent conditions are easy to check. One of such cases is the case of piecewise constant operator coefficient. There are well known sufficient conditions of existence and uniqueness of bounded solution for the case of one jump. In this work, we generalize these results for the case of finite number of jumps of operator coefficient. Moreover, under additional assumption we obtained necessary and sufficient conditions of existence and uniqueness of bounded solution.

scholarly journals Joint 3-D Positioning and Power Allocation for UAV Relay Aided by Geographic Information

2021 ◽  
Author(s):  
Pengfei Yi ◽  
Liang Zhu ◽  
Lipeng Zhu ◽  
Zhenyu Xiao
Keyword(s):  
Power Allocation ◽  
Upper Bound ◽  
Three Dimensional ◽  
Geographic Information ◽  
Base Station ◽  
Lagrangian Multipliers ◽  
Loop Optimization ◽  
Convex Problem ◽  
Communication Links ◽  
Minimum Capacity

<div>In this paper, we study to employ geographic information to address the blockage problem of air-to-ground links between UAV and terrestrial nodes. In particular, a UAV relay is deployed to establish communication links from a ground base station to multiple ground users. To improve communication capacity, we fifirst model the blockage effect caused by buildings according to the three-dimensional (3-D) geographic information. Then, an optimization problem is formulated to maximize the minimum capacity among users by jointly optimizing the 3-D position and power allocation of the UAV relay, under the constraints of link capacity, maximum transmit power, and blockage. To solve this complex non-convex problem, a two-loop optimization framework is developed based on Lagrangian relaxation. The outer-loop aims to obtain proper Lagrangian multipliers to ensure the solution of the Lagrangian problem converge to the tightest upper bound on the original problem. The inner-loop solves the Lagrangian problem by applying the block coordinate descent (BCD) and successive convex approximation (SCA) techniques, where UAV 3-D positioning and power allocation are alternately optimized in each iteration. Simulation results confifirm that the proposed solution signifificantly outperforms two benchmark schemes and achieves a performance close to the upper bound on the UAV relay system.</div>

Polynomial control design for polynomial systems: A non-iterative sum of squares approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1993-2004
Author(s):  
Mohsen Rakhshan ◽  
Navid Vafamand ◽  
Mohammad Mehdi Mardani ◽  
Mohammad-Hassan Khooban ◽  
Tomislav Dragičević
Keyword(s):  
Controller Design ◽  
Time Derivative ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Continuous Stirred Tank Reactor ◽  
Wide Range ◽  
Convex Problem ◽  
Lyapunov Matrix ◽  
Different Chaotic Systems ◽  
Real Time Simulations

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

scholarly journals Energy Efficiency Maximization of Dynamic CoMP-JT Algorithm in Dense Small Cell Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xuefei Peng ◽  
Jiandong Li ◽  
Yifei Xu
Keyword(s):  
Energy Efficiency ◽  
Power Allocation ◽  
Optimal Solution ◽  
Small Cell ◽  
Base Stations ◽  
Maximization Problem ◽  
Second Phase ◽  
User Association ◽  
Coordinated Multipoint ◽  
Convex Problem

We firstly formulate the energy efficiency (EE) maximization problem of joint user association and power allocation considering minimum data rate requirement of small cell users (SUEs) and maximum transmit power constraint of small cell base stations (SBSs), which is NP-hard. Then, we propose a dynamic coordinated multipoint joint transmission (CoMP-JT) algorithm to improve EE. In the first phase, SUEs are associated with the SBSs close to them to reduce the loss of power by the proposed user association algorithm, where the associated SBSs of each small cell user (SUE) form a dynamic CoMP-JT set. In the second phase, through the methods of fractional programming and successive convex approximation, we transform the EE maximization subproblem of power allocation for SBSs into a convex problem that can be solved by proposed power allocation optimization algorithm. Moreover, we show that the proposed solution has a much lower computational complexity than that of the optimal solution obtained by exhaustive search. Simulation results demonstrate that the proposed solution has a better performance.

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