Two-stage Iterative Method Research Articles

Further results on alternating two-stage iterative method

Further results on alternating two-stage iterative method

Decentralized energy market integrating carbon allowance trade and uncertainty balance in energy communities

With sustained attention to carbon neutrality, the personal carbon trading (PCT) scheme has been embraced as an auspicious paradigm for scaling down carbon emissions. To facilitate the simultaneous clearance of energy and carbon allowance inside the energy community while hedging against uncertainty, a joint trading framework is proposed in this article. The energy trading is implemented in a peer-to-peer (P2P) manner without the intervention of a central operator, and the uncertainty trading is materialized through procuring reserve of conventional generators and flexibility of users. Under the PCT scheme, carbon allowance is transacted via a sharing mechanism. Possible excessive carbon emissions due to uncertainty balance are tackled by obliging renewable agents to procure sufficient carbon allowances, following the consumption responsibility principle. A two-stage iterative method consisting of tightening McCormick envelope and alternating direction method of multipliers (ADMM) is devised to transform the model into a mixed-integer second-order cone program (MISOCP) and to allow for a fully decentralized market-clearing procedure. Numerical results have validated the effectiveness of the proposed market model.

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Ultrasound transmission and reflection tomography for nondestructive testing using experimental data

The possibility of reconstructing the velocity structure of inspected objects with a high spatial resolution and high sensitivity in ultrasonic tomographic nondestructive testing within the framework of a wave model has been demonstrated in a real experiment. In this study, a scheme of a tomographic experiment with rotation is proposed, which provides sounding of an inspected object from multiple sides. A tomographic scheme of the experiment with linear antenna transducer arrays operating at a frequency of ∼5 MHz was used. The experiment was conducted on dedicated samples including inserts with different sound propagation velocities. It was shown that the velocity structure and the boundaries of inserts can be reconstructed in the transmission and the reflection schemes. The reconstruction of the velocity structure was formulated as a nonlinear coefficient inverse problem for a scalar wave equation. Efficient iterative methods for its solution on a supercomputer were developed using direct formulas to compute the gradient of the residual functional between the computed and experimentally measured wave field at the detectors. Nonlinearity of the inverse problem of ultrasound tomography leads to multiple local minima of the residual functional. A two-stage iterative method was used for velocity reconstruction. The transmission scheme enables a spatial resolution of approximately 1 mm with a velocity contrast of 2%.

Performance Analysis of Two-Stage Iterative Ensemble Method over Random Oversampling Methods on Multiclass Imbalanced Datasets

Data imbalance occurring among multiclass datasets is very common in real-world applications. Existing studies reveal that various attempts were made in the past to overcome this multiclass imbalance problem, which is a severe issue related to the typical supervised machine learning methods such as classification and regression. But, still there exists a need to handle the imbalance problem efficiently as the datasets include both safe and unsafe minority samples. Most of the widely used oversampling techniques like SMOTE and its variants face challenges in replicating or generating the new data instances for balancing them across multiple classes, particularly when the imbalance is high and the number of rare samples count is too minimal thus leading the classifier to misclassify the data instances. To lessen this problem, we proposed a new data balancing method namely a two-stage iterative ensemble method to tackle the imbalance in multiclass environment. The proposed approach focuses on the rare minority sample’s influence on learning from imbalanced datasets and the main idea of the proposed approach is to balance the data without any change in class distribution before it gets trained by the learner such that it improves the learner’s learning process. Also, the proposed approach is compared against two widely used oversampling techniques and the results reveals that the proposed approach shows a much significant improvement in the learning process among the multiclass imbalanced data.

Convergence of two-stage iterative scheme for [formula omitted]-weak regular splittings of type II

Monotone matrices play a key role in the convergence theory of regular splittings and different types of weak regular splittings. If monotonicity fails, then it is difficult to guarantee the convergence of the above-mentioned classes of matrices. In such a case, K-monotonicity is sufficient for the convergence of K-regular and K-weak regular splittings, where K is a proper cone in Rn. However, the convergence theory of a two-stage iteration scheme in a general proper cone setting is a gap in the literature. Especially, the same study for weak regular splittings of type II (even if in standard proper cone setting, i.e., K=R+n), is open. To this end, we propose convergence theory of two-stage iterative scheme for K-weak regular splittings of both types in the proper cone setting. We provide some sufficient conditions which guarantee that the induced splitting from a two-stage iterative scheme is a K-regular splitting and then establish some comparison theorems. We also study K-monotone convergence theory of the stationary two-stage iterative method in case of a K-weak regular splitting of type II. The most interesting and important part of this work is on M-matrices appearing in the Covid-19 pandemic model. Finally, numerical computations are performed using the proposed technique to compute the next generation matrix involved in the pandemic model. The computation of large PageRank matrices shows that the two-stage Gauss-Seidel method performs better than the Gauss-Seidel methods.

On convergence of two-stage iterative scheme

Climent and Perea [Journal of Computational and Applied Mathematics 58:43–48, 2003; MR2013603] proposed first the convergence theory of two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit the same theory. The first main result provides some sufficient conditions which guarantee that the induced splitting from a two-stage iterative scheme is a proper weak regular splitting. We then establish a few comparison results. Out of these, many are even new in nonsingular matrix setting. Further, we study the monotone convergence theory of the two-stage iterative method. Besides these, we also prove the uniqueness of a proper splitting of a rectangular matrix under certain assumptions.

Antenna Array Directivity Maximization With Sidelobe Level Constraints Using Convex Optimization

New methods for maximizing the directivities of the array antennas are proposed. First, the array pencil beam (PB) directivity maximization problems without or with sidelobe constraints are formulated as convex optimization problems, which are solved optimally to achieve better optimized directivity results, compared with traditional method with radiation intensity maximization only. Then, to deal with the nonconvexity in the wide beam (WB) directivity maximization problem, a novel iterative directivity optimization method based on Taylor expansion of the quadratic function is proposed, and the original nonconvex problem can be efficiently solved by the convex optimization methods in an iterative way. Finally, a two-stage iterative directivity maximization method is further proposed to deal with the sidelobe constraints in the WB directivity maximization problem. Two initial point schemes for the iterative algorithms are studied in detail with the performance comparisons. The two-stage algorithm can be used to yield very good results, even under very wide beamwidth and strict sidelobe constraint conditions. With the proposed methods, the array directivity maximization problems can be solved by the convex optimization methods in a very efficient way. Several representative examples are presented to demonstrate the excellent performance of the proposed methods.

A randomized two-stage iterative method for switched nonlinear systems identification

This paper addresses the identification of discrete time switched nonlinear systems, which are collections of discrete time nonlinear continuous systems (modes) indexed by a finite-valued variable defining the current mode. In particular, we consider the class of Switched Nonlinear AutoRegressive eXogenous (Switched NARX, or SNARX) models, where the continuous dynamics are represented by NARX models. Given a set of input–output data, the identification of a SNARX model for the underlying system involves the simultaneous identification of the mode sequence and of the NARX model associated to each mode, configuring a mixed integer non-convex optimization problem, hardly solvable in practice due to the large combinatorial complexity. In this paper, we propose a black-box iterative identification method, where each iteration is characterized by two stages. In the first stage the identification problem is addressed assuming that mode switchings can occur only at predefined time instants, while in the second one the candidate mode switching locations are refined. This strategy allows to significantly reduce the combinatorial complexity of the problem, thus allowing an efficient solution of the optimization problem. The combinatorial optimization is addressed using a randomized method, whereby the sample-mode map and the SNARX model structure are characterized by a probability distribution, which is progressively tuned via a sample-and-evaluate strategy, until convergence to a limit distribution concentrated on the best SNARX model of the system generating the observed data.

Network transition security for transmission switching

The smart grid with flexible topologies receives intensive attention recently. Transmission switching (TS) alters the power system topology during operation, and has been demonstrated for the advantage of economic and secure operation of power systems. TS includes a chain of sequential switching actions which bring disturbances to the system if the switching actions are not properly designed. Unfortunately, it is not considered or well-studied in existing works. In this paper, a new multi-period TS model that considers the transition security and a two-stage iterative method are proposed. In the TS model, we take into account the fact that only one line is permitted to switch up or down at a time and the security of each switching action is considered. The proposed iterative solution makes the TS model more tractable under AC framework. Case studies on a 6-bus system and the IEEE 57-bus test system have varified the effectiveness of the proposed model. Numerical results show that: ① the consideration of transition security of TS is essential; ② the transition path is directly related to secure and fast the transmission switching; ③ the proposed model and solution method give an effective way to determine the switching sequence and switching timing under transition security criteria.

Greedy subspace pursuit for joint sparse recovery

In the joint sparse recovery, where the objective is to recover a signal matrix X 0 of size n × l or a set Ω of its nonzero row indices from incomplete measurements, subspace-based greedy algorithms improving MUSIC such as subspace-augmented MUSIC and sequential compressive MUSIC have been proposed to improve the reconstruction performance of X 0 and Ω with a computational efficiency even when rank ( X 0 ) ≤ k ≔ | Ω | . However, the main limitation of the MUSIC-like methods is that they most likely fail to recover the signal when a partial support estimate of k − rank ( X 0 ) indices for their input is not fully correct. We proposed a computationally efficient algorithm called two-stage iterative method to detect the remained support (T-IDRS), its special version termed by two-stage orthogonal subspace matching pursuit (TSMP), and its variant called TSMP with sparse Bayesian learning (TSML) by exploiting more than the sparsity k to estimate the signal matrix. They improve on the MUSIC-like methods such that these are guaranteed to recover the signal and its support while the existing MUSIC-like methods will fail in the practically significant case of MMV when rank ( X 0 ) ∕ k is sufficiently small. Numerical simulations demonstrate that the proposed schemes have low complexities and most likely outperform other related methods. A condition of the minimum m required for TSMP to recover the signal matrix is derived in the noiseless case to be applicable to a wide class of the sensing matrix.

Transactive Demand Side Management Programs in Smart Grids with High Penetration of EVs

Due to environmental concerns, economic issues, and emerging new loads, such as electrical vehicles (EVs), the importance of demand side management (DSM) programs has increased in recent years. DSM programs using a dynamic real-time pricing (RTP) method can help to adaptively control the electricity consumption. However, the existing RTP methods, particularly when they consider the EVs and the power system constraints, have many limitations, such as computational complexity and the need for centralized control. Therefore, a new transactive DSM program is proposed in this paper using an imperfect competition model with high EV penetration levels. In particular, a heuristic two-stage iterative method, considering the influence of decisions made independently by customers to minimize their own costs, is developed to find the market equilibrium quickly in a distributed manner. Simulations in the IEEE 37-bus system with 1141 customers and 670 EVs are performed to demonstrate the effectiveness of the proposed method. The results show that the proposed method can better manage the EVs and elastic appliances than the existing methods in terms of power constraints and cost. Also, the proposed method can solve the optimization problem quick enough to run in real-time.

The Cerebral Haemorrhage Anatomical RaTing inStrument (CHARTS): Development and assessment of reliability

PurposeThe causes, risk factors and prognosis of spontaneous intracerebral haemorrhage (ICH) are partly determined by anatomical location (specifically, lobar vs. non-lobar (deep and infratentorial) regions). We systematically developed a rating instrument to reliably classify ICH location. MethodsWe used a two-stage iterative Delphi-style method for instrument development. The resultant Cerebral Haemorrhage Anatomical RaTing inStrument (CHARTS) was validated on CT and MRI scans from a cohort of consecutive patients with acute spontaneous symptomatic ICH by three independent raters. We tested interrater and intrarater reliability using kappa statistics. ResultsOur validation cohort included 227 patients (58% male; median age: 72.4 (IQR: 67.1–74.6)). The interrater reliability for the main analyses (i.e. including any lobar ICH; all deep and infratentorial anatomical categories (lentiform, caudate thalamus; brainstem; cerebellum); and uncertain location) was excellent (all kappa values>0.80) both in pair-wise between-rater comparisons and across all raters. The intrarater reliability was substantial to almost perfect (k=0.83; 95%CI: 0.77–0.88 and k=0.95; 95%CI: 0.92–0.96 respectively). All kappa statistics remained consistent for individual cerebral lobar regions. ConclusionsThe CHARTS instrument can be used to reliably and comprehensively map the anatomical location of spontaneous ICH, and may be helpful for studying important questions regarding causes, risk factors, prognosis, and for stratification in clinical trials.

Two‐stage iterative design for fast filter bank with low complexity

A two-stage iterative method is proposed to design prototype filters for a fast filter bank with low complexity, which is aimed at controlling the optimum ripple magnitude tolerance of each filter according to the overall specifications. This problem is formulated as an optimisation problem for which the total number of multiplications is to be minimised subject to the constrained ripple in the passband and stopband. A two-stage iterative solution is proposed to solve this optimisation problem for the purpose of obtaining impulse response coefficients with low complexity at each stage. Simulations have been conducted to verify the performance of the proposed scheme and show that compared with the original method the proposed scheme can reduce the number of multiplications by about 20.02%.

Efficiently implementable iterative methods for linear elliptic variational inequalities with constraints on the gradient of solution

We construct and investigate a new iterative solution method for a finite-dimensional constrained saddle point problem. The results are applied to prove the convergence of different iterativemethods formesh approximations of variational inequalities with constraints on the gradient of solution. In particular, we prove the convergence of two-stage iterative methods. The main advantage of the proposed methods is the simplicity of their implementation. The numerical testing demonstrates high convergence rate of the methods.

Non-stationary Parallel Multisplitting Two-Stage Iterative Methods with Self-AdaptiveWeighting Schemes

Non-stationary Parallel Multisplitting Two-Stage Iterative Methods with Self-AdaptiveWeighting Schemes

Source Power Allocation and Relaying Design for Two-Hop Interference Networks with Relay Conferencing

In this paper, we consider a two-hop interference network, which consists of two source-destination pairs and two relay nodes connected with signal-to-noise ratio (SNR) limited out-of-band conferencing links. Assuming that the amplify-and-forward (AF) relaying scheme is adopted, this network is shown to be equivalent to a two-user interference channel (IC). By deploying two IC decoding schemes, i.e., single-user decoding and joint decoding, respectively, we characterize the achievable rate regions with a two-stage iterative optimization method: First, we fix the source power pair and maximize the sum rate over the relay combining vector; second, we fix the relay combining vector and optimize the source power pair. Specifically, for single-user decoding, we design a new routine to compute the optimal solution for the first subproblem, which is more efficient than the existing scheme; and for the second subproblem, we develop an iterative algorithm, with the closed-form solution for each iteration. Furthermore, it is revealed that the AF scheme with relay conferencing achieves the full degree-of-freedom (DoF), which outperforms the case without relay conferencing. Finally, simulation results show that relay conferencing can significantly improve the system performance under certain channel conditions.

Parallel multisplitting two-stage iterative methods with general weighting matrices for non-symmetric positive definite systems

In this work, we propose a new parallel multisplitting iterative method for non-symmetric positive definite linear systems. Based on optimization theory, the new method has two great improvements; one is that only one splitting needs to be convergent, and the other is that the weighting matrices are not scalar and nonnegative matrices. The convergence of the new parallel multisplitting iterative method is discussed. Finally, the numerical results show that the new method is effective.

LDA boost classification: boosting by topics

AdaBoost is an efficacious classification algorithm especially in text categorization (TC) tasks. The methodology of setting up a classifier committee and voting on the documents for classification can achieve high categorization precision. However, traditional Vector Space Model can easily lead to the curse of dimensionality and feature sparsity problems; so it affects classification performance seriously. This article proposed a novel classification algorithm called LDABoost based on boosting ideology which uses Latent Dirichlet Allocation (LDA) to modeling the feature space. Instead of using words or phrase, LDABoost use latent topics as the features. In this way, the feature dimension is significantly reduced. Improved Naive Bayes (NB) is designed as the weaker classifier which keeps the efficiency advantage of classic NB algorithm and has higher precision. Moreover, a two-stage iterative weighted method called Cute Integration in this article is proposed for improving the accuracy by integrating weak classifiers into strong classifier in a more rational way. Mutual Information is used as metrics of weights allocation. The voting information and the categorization decision made by basis classifiers are fully utilized for generating the strong classifier. Experimental results reveals LDABoost making categorization in a low-dimensional space, it has higher accuracy than traditional AdaBoost algorithms and many other classic classification algorithms. Moreover, its runtime consumption is lower than different versions of AdaBoost, TC algorithms based on support vector machine and Neural Networks.

Some results on convergence of two-stage iterative methods for symmetric positive definite linear systems

Parallel iterative algorithms for linear systems have become an important area in high performance computation. This paper studies two-stage iterative methods for symmetric positive definite linear systems. An estimate of minimum inner iterative number is obtained for convergence of stationary iterative methods. The convergent range of relaxation factor of relaxed two-stage iterative methods is decided by the minimums of eigenvalues of inner and outer iteration matrices.