Cyclic Iterative Algorithm Research Articles

Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed-Point Problems

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.

Strong convergence of split equality variational inequality, variational inclusion, and multiple sets fixed point problems in Hilbert spaces with application

This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem.

Simulation of Pitting Corrosion Under Stress Based on Cellular Automata and Finite Element Method

Abstract A new cellular automaton (CA) program was written in python language to simulate the random pitting evolution process, which can not only obtain a variety of different corrosion products but also obtain a variety of common corrosion morphologies on the surface of metal pipes, bridge steel members, etc. In addition, commercial finite element (FE) software abaqus was redeveloped using python scripting language, and the FE mesh with the same size as the cellular mesh was established based on the consistent mesh algorithm, which ensured the efficiency and accuracy of the cyclic iterative algorithm. The stress and strain fields were calculated in real-time by applying the force load, the dissolution probability parameter P was updated in python according to the force-chemical coupling model, and a new corrosion morphology was obtained in python. At the same time, the birth and death element method was applied in abaqus to kill the corrosion elements in this iterative step simultaneously, and the new stress-strain field was recalculated in abaqus. The established consistent grid modeling strategy and cyclic iterative algorithm can significantly improve the solving efficiency of pitting evolution under the coupled action of corrosive medium and load. The results show that the stress concentration caused by pit expansion and the corrosion acceleration effect dominated by plastic deformation will promote each other, leading to the continuous growth of pitted pits. The established modeling strategy and cyclic iterative algorithm can significantly improve the solving efficiency of pitting evolution under the coupled action of corrosive medium and load.

Optimizing an Algorithm Designed for Sparse-Frequency Waveforms for Use in Airborne Radars

Low-frequency bands are an important way to realize stealth target detection for airborne radars. However, in a complex electromagnetic environment; when low-frequency airborne radar operates over land, it will inevitably encounter a lot of unintentional communication and intentional interference, while effective suppression of interference can not be achieved only through the adaptive processing of the receiver. To solve this problem, this paper proposes optimizing an algorithm designed for sparse-frequency waveforms for use in airborne radars. The algorithm establishes a joint objective function based on the criteria of minimizing waveform energy in the spectrum stopband and minimizing the integrated sidelobe level of specified range cells. The waveform is optimized by a cyclic iterative algorithm based on the Fast Fourier Transform (FFT) operation. It can ensure the frequency domain stopband constraint to realize the effective suppression of main-lobe interference while forming lower-range sidelobes at specified range cells to improve the ability to detect dim targets. Theoretical analysis and simulation results have shown that the algorithm has good anti-interference performance.

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

A cyclic iterative method for solving the system of split equality zero-point problems

ABSTRACT The purpose of this paper is to introduce a new cyclic iterative algorithm for finding a solution to the system of split equality zero-point problems in Hilbert spaces. The strong convergence of the proposed algorithm is established under some mild conditions. Moreover, this algorithm does not depend on the norm of the transfer mappings. Some applications of the main theorem to the related problems are also presented.

On Tethered UAV-Assisted Heterogeneous Network

Unmanned aerial vehicle (UAV)-assisted heterogeneous network has drawn great research interests as it can significantly improve the capacity and coverage of the cellular networks. An UAV can act as a flying base station (BS) or a relay when the regular terrestrial infrastructure is malfunctioned or overloaded. However, the deployment of UAV-mounted communication infrastructure is confined by the limited on-board energy and short battery life. To prolong the lifetime of each UAV, connecting it with a ground charging station (GCS) through a tether could be a promising and feasible solution. In this paper, we aim to maximize the sum rate of all users by jointly optimizing the user association, resource allocation and placement of the GCSs and the aerial UAVs. In addition, the constraint of each user's quality of service (QoS) requirement and total available resource are considered. To tackle this problem, we propose a cyclic iterative algorithm to efficiently obtain suboptimal solutions. Specifically, the primal problem is decomposed into three subproblems, i.e., the TUAV placement problem, the resource allocation problem and the user association problem. Then, the three sub-problems are alternately and iteratively optimized by using the outputs of the first two as the input for the third. Numerical experiments demonstrate that our proposed algorithm outperforms baseline algorithms under different setups.

Latency Aware 3D Placement and User Association in Drone-Assisted Heterogeneous Networks With FSO-Based Backhaul

Drone Base Station (DBS) is expected to play an important role in next generation cellular networks due to its maneuverability in establishing air-to-ground Line of Sight (LoS) links. Working as a mobile relay node between the Macro Base Station (MBS) and the ground users, the DBS can significantly reduce the latency of ground users by offloading traffic loads from the MBS to the DBS since a better channel condition can be provided. In this paper, we focus on how to determine the 3D location of the DBS, the user association and the bandwidth allocation policy between the MBS and the DBS in order to minimize the total average latency ratio of all users with the constraint of each user's QoS requirement and total available bandwidth. The formulated problem is a mixed integer nonconvex optimization problem, a very challenging and difficult problem. We propose a cyclic iterative algorithm to efficiently solve it by decomposing the primal problem into two subproblems, i.e., the user association and bandwidth allocation problem and the 3D DBS placement problem. In each iteration, the two sub-problems are alternatively optimized by using the output of one as the input for the other. Numerical simulation results demonstrate the significant latency ratio reduction of our proposed algorithm as compared to other baseline schemes.

The coupled model of wellbore temperature and pressure for variable gradient drilling in deep water based on dynamic mass flow

Variable gradient drilling in deep water is a new drilling method of using separators to separate hollow glass spheres (Referred to as HGS, it is the glass microbeads with low density less than 1.0 kg/m3, and the worse thermal conductivity) from the drill string directly into the annulus, which can form multiple gradients of drilling fluid density in annulus. This method can better deal with the problem of narrow pressure window in deep water drilling. At present, there are few studies on the wellbore temperature and pressure distribution of this technology, and the separation efficiency of the existing separator is too low to achieve variable gradient. The purpose of this paper is to develop a new separator to improve the separation efficiency, and to study the coupled wellbore temperature and pressure field of variable gradient drilling based on dynamic mass flow. Firstly, indoor simulated experiments were used to study the separation efficiency of the newly developed filter separator, and based on the separation efficiency, wellbore flow theory and the first law of thermodynamics, the dynamic mass flow at the location of the separator were fully considered. Considering the influence of wellbore temperature and pressure on thermophysical parameters, a coupled model of wellbore temperature and pressure was established based on dynamic mass flow. Then the model was discretized and solved by finite difference method and cyclic iterative algorithm. Further, this model was verified based on the existing models and drilling site data. Finally, the effects of key parameters in variable gradient drilling on the annulus temperature, pressure and fluid density were studied. The results show that the filter separator has high feasibility, and the separation efficiency can reach 95%–98.5%. Compared with conventional drilling, distribution curve of the temperature, pressure and the mixture density in annulus of the filter separator section has obvious inflection points in variable gradient drilling, and the number of inflection points is equal to the number of separators. What's more, the number and location of separators, the HGS volume fraction, pump flow rate, and the HGS density have significant effects on the annulus temperature and pressure. This research can significantly improve the feasibility of variable gradient drilling in deep water and provide a theoretical reference for further research in this direction.

A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

3D Drone Base Station Placement and Resource Allocation With FSO-Based Backhaul in Hotspots

Deploying a Drone Base Station (DBS) over a hotspot area is a promising solution to improve the user Quality of Service (QoS) by helping the Macro Base Station (MBS) transmit traffic to the users. Essentially, the DBS, which works as a relay node between the users and the MBS, can increase the users' data rates by virtue of more likely short-distance Line of Sight (LoS) communication links. Furthermore, deploying DBS is more cost-effective and flexible as compared to deploying small cells. The DBS can employ Free Space Optical (FSO) links for backhauling between the DBS and the MBS. In this paper, we study the 3D deployment and resource allocation of a DBS in a given hotspot area with the objective of maximizing the throughput in the access link under the constraint of user QoS, the capacity of the backhaul link, and total available bandwidth and power. To solve the problem, we first decompose the primal problem into two subproblems, i.e., the 3D DBS placement problem and the resource allocation problem. Second, we propose a cyclic iterative algorithm to solve the two sub-problems separately and use the output of one as the input of the other. The performance of the algorithm is demonstrated via extensive simulations.

Adaptive optimal waveform design algorithm based on frequency‐stepped chirp signal

In this study, the authors propose an adaptive optimal waveform design algorithm, based on a frequency-stepped chirp signal with arbitrary sub-pulse bandwidths and chirp slopes. The waveform is designed to maximise the signal-to-interference-plus-noise ratio at the receiver. The integral sidelobe level of an autocorrelation function is constrained at a low level, thereby increasing the detection probability of the weak echoes reflected from dim targets. An energy constraint and a low peak-to-average power ratio constraint are also taken into account owing to the flexible power allocation for interference suppression. By doing so, the radar system improves the efficiency of the transmitter power resources and avoids the non-linear effects of the power amplifier. What is more, a cyclic iterative algorithm is employed to solve the optimisation problem. At last, numerical simulation results evaluate the effectiveness of the designed waveform compared with a linear frequency modulation signal, resulting in a great improvement in the target detection performance.

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Global convergence and ascent property of a cyclic algorithm used for statistical analysis of crash data

In this paper, we consider an estimation algorithm called cyclic iterative algorithm (CA) that is used in statistics to estimate the unknown vector parameter of a crash data model. We provide a theoretical proof of the global convergence of the CA that justifies the good numerical results obtained in early numerical studies of this algorithm. We also prove that the CA is an ascent algorithm, what ensures its numerical stability. Keywords: Iterative method, Maximum likelihood, cyclic algorithm, global convergence, road safety AMS 2010 Mathematics Subject Classification : 62-04, 62F10, 62H12, 62P99

Research and Application of SO2 Concentration Monitoring Algorithm in Flue Gas

Abstract This paper mainly focuses on the concentration calculation of SO2 in flue gas. There are many methods for smoke detection. First of all, this paper mainly introduces the basic Differential Optical Absorption Spectroscopy technology. Then, in order to solve the problem of overlapping absorption between different gases in the flue gas, this paper use cyclic iteration algorithm to measure the concentration of SO2. It is concluded that the basic DOAS algorithm has a large error for the concentration measurement of mixed gas with overlapping absorption, the he error is above 25%. However, the cyclic iterative algorithm has a good effect on processing with it which can get a more stable result after three iterations, and the measurement error can be controlled finally within 2%.

Joint optimal flood control operation of large scale mixed reservoirs

With the reservoir construction gradually completed, joint operation of reservoir groups is an important measure to realize reservoir flood control potential,but when the river basin is large, the flood channel routing and time-lag cannot be simplified, in addition, the curse of dimensionality is very difficult for model solving With the expansion of the number of reservoirs. These factors restrict the application of joint operation of large scale mixed reservoirs.In this study, The DP-POA cyclic iterative algorithm which is based on large scale system decomposed-coordinating method was proposed to solve the optimal problem considering the flood routing and time-lag.The upper Yangtze River is selected as a case study. 6 reservoirs, including the Three Gorges Reservoir(TGR)、Xiangjiaba Reservoir(XJB)、Xiluodu Reservoir (XLD)、 Pubugou Reservoir (PBG)、Goupitan Reservoir (GPT) and Tingzikou Reservoir (TZK)are taken into accounts.Compared with current operation of reservoirs independent,results demonstrate that the method can effectively reduce the maximum operating water level of TGR and flood diversion in the lower reaches of the TGR. Therefore, the safety of the flood control points along the river has been largely improved based on the proposed method.

Strong convergence of a cyclic iterative algorithm for split common fixed-point problems of demicontractive mappings

Strong convergence of a cyclic iterative algorithm for split common fixed-point problems of demicontractive mappings

A cyclic iterative approach and its modified version to solve coupled Sylvester-transpose matrix equations

Recently, Tang et al. [Numer Algorithms. 2014;66(2):379–397] have offered a cyclic iterative method for determining the unique solution of the coupled matrix equationsAnalogues to the gradient-based algorithm, the proposed algorithm relies on a fixed parameter whereas it has wider convergence region. Nevertheless, the application of the algorithm to find the centro-symmetric solution of the mentioned problem has been left as a project to be investigated and the optimal value for the fixed parameter has not been derived. In this paper, we focus on a more general class of the coupled linear matrix equations that incorporate the mentioned ones in the earlier refereed work. More precisely, we first develop the authors’ propounded algorithm to resolve our considered coupled linear matrix equations over centro-symmetric matrices. Afterwards, we disregard the restriction of the existence of the unique (centro-symmetric) solution and also modify the authors’ algorithm by applying an oblique projection technique which allows to produce a sequence of approximate solutions which gratify an optimality property. Numerical results are reported to confirm the validity of the established results and to demonstrate the superior performance of the modified version of the cyclic iterative algorithm.

Weak and Strong Convergence Theorems for the Multiple-Set Split Equality Common Fixed-Point Problems of Demicontractive Mappings

We consider mixed parallel and cyclic iterative algorithms in this paper to solve the multiple-set split equality common fixed-point problem which is a generalization of the split equality problem and the split feasibility problem for the demicontractive mappings without prior knowledge of operator norms in real Hilbert spaces. Some weak and strong convergence results are established. The results obtained in this paper generalize and improve the recent ones announced by many others.

Several iterative algorithms for solving the split common fixed point problem of directed operators with applications

In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms.