convex optimization problem
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Author(s):  
Oscar Danilo Montoya ◽  
Carlos Alberto Ramírez-Vanegas ◽  
Luis Fernando Grisales-Noreña

<p>The problem of parametric estimation in photovoltaic (PV) modules considering manufacturer information is addressed in this research from the perspective of combinatorial optimization. With the data sheet provided by the PV manufacturer, a non-linear non-convex optimization problem is formulated that contains information regarding maximum power, open-circuit, and short-circuit points. To estimate the three parameters of the PV model (i.e., the ideality diode factor (a) and the parallel and series resistances (R<sub>p</sub> and R<sub>s</sub>)), the crow search algorithm (CSA) is employed, which is a metaheuristic optimization technique inspired by the behavior of the crows searching food deposits. The CSA allows the exploration and exploitation of the solution space through a simple evolution rule derived from the classical PSO method. Numerical simulations reveal the effectiveness and robustness of the CSA to estimate these parameters with objective function values lower than 1 × 10<sup>−28</sup> and processing times less than 2 s. All the numerical simulations were developed in MATLAB 2020a and compared with the sine-cosine and vortex search algorithms recently reported in the literature.</p>


Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Hongxia Zheng ◽  
Chiya Zhang ◽  
Yatao Yang ◽  
Xingquan Li ◽  
Chunlong He

We maximize the transmit rate of device-to-device (D2D) in a reconfigurable intelligent surface (RIS) assisted D2D communication system by satisfying the unit-modulus constraints of reflectin elements, the transmit power limit of base station (BS) and the transmitter in a D2D pair. Since it is a non-convex optimization problem, the block coordinate descent (BCD) technique is adopted to decouple this problem into three subproblems. Then, the non-convex subproblems are approximated into convex problems by using successive convex approximation (SCA) and penalty convex-concave procedure (CCP) techniques. Finally, the optimal solution of original problem is obtained by iteratively optimizing the subproblems. Simulation results reveal the validity of the algorithm that we proposed to solve the optimization problem and illustrate the effectiveness of RIS to improve the transmit rate of the D2D pair even with hardware impairments.


Sensors ◽  
2022 ◽  
Vol 22 (1) ◽  
pp. 370
Author(s):  
Ruijie Guo ◽  
Chunling Fu ◽  
Yong Jin ◽  
Zhentao Hu ◽  
Lin Zhou

This paper considers the physical layer security (PLS) of a simultaneous wireless information and power transfer (SWIPT) relay communication system composed of a legitimate source–destination pair and some eavesdroppers. Supposing a disturbance of channel status information (CSI) between relay and eavesdroppers in a bounded ellipse, we intend to design a robust beamformer to maximum security rate in the worst case on the constraints of relay energy consumption. To handle this non-convex optimization problem, we introduce a slack variable to transform the original problem into two sub-problems firstly, then an algorithm employing a semidefinite relaxation (SDR) technique and S-procedure is proposed to tackle above two sub-problems. Although our study was conducted in the scene of a direct link among source, destination, and eavesdroppers that is non-existing, we demonstrate that our conclusions can be easily extended to the scene for which a direct link among source, destination and eavesdroppers exist. Numerical simulation results compared with the benchmark scheme are provided to prove the effectiveness and superior performance of our algorithm.


Author(s):  
Ryan J. Kinnear ◽  
Ravi R. Mazumdar ◽  
Peter Marbach

We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.


Author(s):  
Bo Fang ◽  
Hu Jianzhong ◽  
Cheng Yang ◽  
Yudong Cao ◽  
Minping Jia

Abstract Blind deconvolution (BD) is an effective algorithm for enhancing the impulsive signature of rolling bearings. As a convex optimization problem, the existing BDs have poor optimization performance and cannot effectively enhance the impulsive signature excited by weak faults. Moreover, the existing BDs require manual derivation of the calculation process, which brings great inconvenience to the researcher's personalized design of the maximization criterion. A new BD algorithm based on backward automatic differentiation (BAD) is proposed, which is named BADBD. The calculation process does not require manual derivation so a general solution of BDs based on different maximization criteria is realized. BADBD constructs multiple cascaded filters to filter the raw vibration signal, which makes up for the deficiency of single filter performance. The filter coefficients are determined by Adam algorithm, which improves the optimization performance of the proposed BADBD. BADBD is compared with classic BDs by synthesized and real vibration signals. The results reveal superior capability of BADBD to enhance the impulsive signature and the fault diagnosis performance is significantly better than the classic BDs.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Liang Xue ◽  
Yao Ma ◽  
Miao Zhang ◽  
Wanqiang Qin ◽  
Jin-Long Wang ◽  
...  

In this paper, the optimal beamforming problem of multi-input single-output (MISO) cognitive radio (CR) downlink networks with simultaneous wireless information and power transfer is studied. Due to the nonconvexity of the objective function, the considered nonconvex optimization problem is firstly transformed to an equivalent subtraction problem and then an approximated convex optimization problem is obtained by using the successive convex approximation (SCA). When the instantaneous channel state information (CSI) of the eavesdropping link is unknown to the legitimate transmitter, another interruption-constrained energy efficiency optimization problem is proposed and the Bernstein-type inequality (BTI) is used to conservatively approximate the probability constraint. The paper proposes a two-level iterative algorithm based on Dinkelbach to find the optimal solution of the EE maximization problem. Numerical results validate the effectiveness and convergence of the proposed algorithm.


Author(s):  
Gabriela Kováčová ◽  
Birgit Rudloff

AbstractIn this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the solution to that problem also solves the convex projection (and vice versa), which is analogous to the result in the polyhedral convex case considered in Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016). In practice, however, one can only compute approximate solutions in the (bounded or self-bounded) convex case, which solve the problem up to a given error tolerance. We will show that for approximate solutions a similar connection can be proven, but the tolerance level needs to be adjusted. That is, an approximate solution of the convex projection solves the multi-objective problem only with an increased error. Similarly, an approximate solution of the multi-objective problem solves the convex projection with an increased error. In both cases the tolerance is increased proportionally to a multiplier. These multipliers are deduced and shown to be sharp. These results allow to compute approximate solutions to a convex projection problem by computing approximate solutions to the corresponding multi-objective convex optimization problem, for which algorithms exist in the bounded case. For completeness, we will also investigate the potential generalization of the following result to the convex case. In Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016), it has been shown for the polyhedral case, how to construct a polyhedral projection associated to any given vector linear program and how to relate their solutions. This in turn yields an equivalence between polyhedral projection, multi-objective linear programming and vector linear programming. We will show that only some parts of this result can be generalized to the convex case, and discuss the limitations.


2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Cesar A. Agón ◽  
Márk Mezei

Abstract Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.


2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Fangyu Ren ◽  
Huotao Gao ◽  
Lijuan Yang ◽  
Sang Zhou

This paper establishes a distributed multistatic sky-wave over-the-horizon radar (DMOTHR) model and proposes a semidefinite relaxation positioning (SDP) algorithm to locate marine ship targets. In the DMOTHR, it is difficult to locate the target due to the complexity of the signal path propagation. Therefore, this paper uses the ionosphere as the reflector to convert the propagation path from a polyline to a straight line for establishing the model, and then the SDP algorithm will be used to transform a highly nonlinear positioning optimization problem into a convex optimization problem. Finally, it is concluded through the simulations that the SDP algorithm can obtain better positioning accuracy under a certain Doppler frequency error and ionospheric measurement error.


Electronics ◽  
2021 ◽  
Vol 10 (20) ◽  
pp. 2536
Author(s):  
Zhixiang Deng ◽  
Yan Pan

In this paper, we study a simultaneous wireless information and power transfer (SWIPT) system aided by the intelligent reflecting surface (IRS) technology, where an AP transmits confidential information to the legitimate information receiver (IR) in the presence of an energy harvesting (EH) receiver that could be a potential eavesdropper. We aim to maximize the secrecy rate at the legitimate IR by jointly optimizing the information beamforming vector and the energy transfer beamforming vector at the access point (AP), and the phase shift matrix at the IRS, subject to the minimum harvested power required by the EH receiver. The semi-definite relaxation (SDR) approach and the alternating optimization (AO) method are proposed to convert the original non-convex optimization problem to a series of semi-definite programs (SDPs), which are solved iteratively. Numerical results show that the achievable secrecy rate of the proposed IRS-assisted SWIPT system is higher than that of the SWIPT system without the assistance of the IRS.


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