Convergence Of Algorithm Research Articles

Convergence of a TPFA finite volume scheme for nonisothermal immiscible compressible two-phase flow in porous media

This paper presents and analyzes a finite volume scheme for a fully degenerate parabolic system modeling the compressible two-phase flow, such as water-gas, problem in porous media considering the effects of temperature. The problem is written in terms of the phase formulation, i.e. the saturation of one phase, the pressure of the second phase and the temperature are primary unknowns. We use a first-order time implicit Euler scheme. The spatial discretization uses a fully coupled fully implicit cell-centered two-point flux approximation scheme where upwinding of the flux across an interface between two control volumes is performed for each fluid phase. Under physically relevant assumptions on the data, we prove the maximum principle for both saturation and temperature. We obtain a priori estimates and we show that the discrete problem is well posed. Also, we exploit various a priori estimates as well as compactness arguments to establish the convergence of the numerical scheme toward the weak solution. The open-source platform DuMuX was employed for the implementation of the developed algorithm based on the above scheme. Numerical result are presented to demonstrate the efficiency of this scheme. The test addresses the evolution in 2D of CO2 injection into a layered aquifer. The algorithm's convergence with first order is validated by our numerical results, which support the theoretical results. To our best knowledge, this is the first convergence result of a finite volume scheme in the case of nonisothermal immiscible compressible two-phase flow in porous media.

New method for calculating the windward area of irregular fragments

Average windward area is an important index for calculating the trajectory, velocity attenuation and terminal effect of explosive fragments. In order to solve the problems that existing theoretical method cannot calculate windward area of irregular fragment and experiment method is not convenient for automatic calculation and has low accuracy, a Monte Carlo subdivision projection simulation algorithm is proposed. The average windward area of arbitrary shaped fragments can be obtained with coordinate translation, random rotation, plane projection, convex-hull triangulation, concave boundary searching and sorting with maximum edge length constraint, subdivision area calculation, and averaging by thousands of cycles. Results show that projection area obtained by the subdivision projection algorithm is basically the same as that obtained by software method of computer aided design. Moreover, the maximum calculation error of the algorithm is less than 7%, and its accuracy is much higher than that of the equivalent ellipsoid method. The average windward area calculated by the Monte Carlo subdivision projection simulation algorithm is consistent with theoretical formula for prefabricated fragments, and the error is less than 3%. The convergence and accuracy of the Monte Carlo subdivision projection algorithm are better than those of the icosahedral uniform orientation method.

One-step incremental multi-view spectral clustering based on graph linkage learning

Most traditional multi-view spectral clustering algorithms involve two separate steps: solving the spectral embedding matrix and clustering, which may introduce errors during the clustering process. Moreover, in practical applications, the number of available views may increase over time, and the approach of re-fusing all views in each computation would result in elevated computational costs. In this paper, we propose a novel model: One-step Incremental Multi-view Spectral Clustering based on Graph Linkage learning (OIMvSC). OIMvSC only needs to store the consensus spectral embedding matrix and the consensus label matrix of all previous views and combines them with the spectral embedding matrix of the newly available view to solve the fused consensus spectral embedding matrix and consensus label matrix. To further enhance clustering performance, OIMvSC introduces graph linkage learning, which reduces erroneous connections between clusters while preserving correct connections within clusters. A convergent iterative algorithm for solving OIMvSC is proposed. Experimental results demonstrate that OIMvSC exhibits excellent clustering performance.

Process design and adsorbent screening of VSA and exchanger type VTSA for flue gas CO2 capture

Carbon capture, as a core technology for mitigating greenhouse gas emissions, the greatest challenge is the balance between separation performance and energy consumption. This study seeks to evaluate and screen the separation performance and energy consumption of four typical adsorbents (13X, Mg-MOF-74, activated carbon, and Lewatit VP OV 1065) in vacuum temperature swing adsorption (VTSA) and vacuum swing adsorption (VSA) through optimization approach, which will support in-depth research and decision-making on adsorption processes. A non-isothermal non-adiabatic numerical model was carried out to describe a novel 4-bed 10-step VTSA cycle developed on an exchange type adsorption unit (ETAU), and the model was validated by binary breakthrough and temperature swing experiments. A 4-bed 10-step VSA cycle was in turn established and investigated. Parametric analysis of the two cycles was performed by varying the operating variables including feed gas flow rate, recycle time, and purge-to-feed ratio. Process optimization of the multiplicative fraction evaluation function, simultaneously considering purity, recovery, and productivity, was achieved using a dual convergence algorithm. Results showed that all four adsorbents could achieve more than 90 % purity and recovery on the VTSA process employing the ETAU for post-combustion carbon capture, and the separation performance was substantially superior to that of the VSA cycle. Mg-MOF-74 obtained a CO2 product with 97.90 % purity, 98.48 % recovery, and 5.48 mol/kgads/hr productivity at a desorption temperature of 383.15 K; it has a specific heat consumption of 1.45 GJth/ton and a specific power consumption of 0.55 GJel/ton. The total energy consumption of 13X was slightly lower than that of amine adsorbents, giving 95.00 % purity, 97.60 % recovery, and 1.91 mol/kgads/hr productivity. Relatively low desorption temperature is expected to introduce ultra-low-grade waste heat for partial heat source substitution, contributing to the energy sustainability of adsorption carbon capture technology.

Differentiated Security Requirements: An Exploration of Microservice Placement Algorithms in Internet of Vehicles

In recent years, microservices, as an emerging technology in software development, have been favored by developers due to their lightweight and low-coupling features, and have been rapidly applied to the Internet of Things (IoT) and Internet of Vehicles (IoV), etc. Microservices deployed in each unit of the IoV use wireless links to transmit data, which exposes a larger attack surface, and it is precisely because of these features that the secure and efficient placement of microservices in the environment poses a serious challenge. Improving the security of all nodes in an IoV can significantly increase the service provider’s operational costs and can create security resource redundancy issues. As the application of reinforcement learning matures, it is enabling faster convergence of algorithms by designing agents, and it performs well in large-scale data environments. Inspired by this, this paper firstly models the placement network and placement behavior abstractly and sets security constraints. The environment information is fully extracted, and an asynchronous reinforcement-learning-based algorithm is designed to improve the effect of microservice placement and reduce the security redundancy based on ensuring the security requirements of microservices. The experimental results show that the algorithm proposed in this paper has good results in terms of the fit of the security index with user requirements and request acceptance rate.

Approximate weak optimality conditions in multiobjective generalized Nash equilibrium problems

A multiobjective generalized Nash equilibrium problem (MGNEP) is a Nash equilibrium problem with constraints that include multiobjective games. We focus in this paper on examining the approximate Karush–Kuhn–Tucker (KKT) conditions for MGNEPs and their impact on the global convergence of algorithms. To begin, we define standard approximate weak KKT (standard-AWKKT) conditions for MGNEPs. We demonstrate that every weak efficient solution meets the standard-AWKKT condition. As these optimality conditions are strong, we propose a new set of approximate weak KKT conditions, specifically tailored for MGNEPs, and show their convergence towards weak KKT points provided a cone-continuity property is satisfied. It is important to note that while these newly introduced approximate weak KKT conditions do not serve as optimality conditions for general MGNEPs, we illustrate that they hold true for the special case of a weak variational equilibrium point in a jointly convex MGNEP. Finally, we propose an enhanced Lagrangian-type algorithm for estimating an approximate weak KKT of an MGNEP and demonstrate its global convergence.

A modified two-parameter scaled Broyden-type algorithm for unconstrained optimization problems

The Broyden-type algorithm is one of the most effective quasi-Newton methods for solving unconstrained optimization problems. However, the study of the global convergence of the Broyden-type algorithm is not enough. Motivated by Andrei (J. Comput. Appl. Math. 332: 26–44, 2018), we present a modified two-parameter scaled Broyden-type algorithm. Some approaches are used in the designed method: (1) we introduce a modified Broyden-type formula with two parameters; (2) we use approximated parameter settings to reduce the effect of eigenvalues of sequence {Bk}; (3) we propose a modified weak Wolfe–Powell line search technique with projection technique to avoid using failed search direction. The parameters of our study have the same functionality, that of correcting the structure of the eigenvalues of the approximate Hessian matrix. The difference is in the approach of 4-term Broyden updates instead of BFGS. Numerical performance shows that the modified Broyden-type algorithm is competitive with the classical Broyden approach.

High utility itemsets mining based on hybrid harris hawk optimization and beluga whale optimization algorithms

The commonly used high utility itemsets mining method for massive data is the intelligent optimization algorithm. In this paper, the WHO (Whale-Hawk Optimization) algorithm is proposed by integrating the harris hawk optimization (HHO) algorithm with the beluga whale optimization (BWO) algorithm. Additionally, a whale initialization strategy based on good point set is proposed. This strategy helps to guide the search in the initial phase and increase the diversity of the population, which in turn improve the convergence speed and algorithm performance. By applying this improved algorithm to the field of high utility itemsets mining, it provides new solutions to optimization problems and data mining problems. To evaluate the performance of the proposed WHO, a large number of experiments are conducted on six datasets, chess, connect, mushroom, accidents, foodmart, and retail, in terms of convergence, recall rates, and runtime. The experimental results show that the convergence of the proposed WHO is optimal in five datasets and has the shortest runtime in all datasets. Compared to PSO, AF, BA, and GA, the average recall rate in the six datasets increased by 32.13%, 49.95%, 12.15%, and 16.24%, respectively.

Mixture correntropy-based robust distance metric learning for classification

Metric learning is a branch of machine learning that aims to learn from the given training data a valid distance metric, with which the similarity between samples can be more effectively evaluated for classification. Metric learning has attracted significant attention, and a large number of models have been proposed in the past few years. However, the traditional methods adopt hinge loss which easily leads to noise sensitivity and instability. In this paper, to improve the robustness performance, we develop a mixture correntropy criterion where two Laplacian kernel functions are combined as the kernel function and induce a more general nonconvex robust loss function by the mixture correntropy. The properties related to the loss function are analysed and presented. The induced loss amalgamates the superiors of the state-of-the-art robust loss functions and is more effective. With this induced loss, we establish a robust metric learning model (called MCML) and design an effective iterative algorithm to optimize the nonconvex challenging problem. The computational complexity and convergence of algorithm are discussed in theory. Furthermore, a boosting version of MCML (BMCML) is derived, where the low-rank basis learning is jointly optimized with the metric to better uncover the data structure. Finally, extensive experiments are conducted on artificial datasets, UCI benchmark datasets and image datasets. The experimental results verify the robustness and effectiveness of the proposed methods.

Weak and Strong Convergence of Split Douglas-Rachford Algorithms for Monotone Inclusions

We are concerned in this paper with the convergence analysis of the primal-dual splitting (PDS) and the split Douglas-Rachford (SDR) algorithms for monotone inclusions by using an operator-oriented approach. We shall show that both PDS and SDR algorithms can be driven by a (firmly) nonexpansive mapping in a product Hilbert space. We are then able to apply the Krasnoselskii-Mann and Halpern fixed point algorithms to PDS and SDR to get weakly and strongly convergent algorithms for finding solutions of the primal and dual monotone inclusions. Moreover, an additional projection technique is used to derive strong convergence of a modified SDR algorithm.

Causality Analysis of the Green Ammonia Synthesis Process Using the Convergent Cross Mapping Algorithm

Causality Analysis of the Green Ammonia Synthesis Process Using the Convergent Cross Mapping Algorithm

Edge-based distributed primal–dual algorithms for seeking generalized Nash equilibria

This paper introduces two novel distributed algorithms aimed at finding the generalized Nash equilibria (GNE) in noncooperative games. To tackle this, we utilize the variational inequality framework, transforming the noncooperative game into the challenge of identifying the zeros of a sum of monotone operators. Within noncooperative games, the decisions made by individual players are interlinked via shared affine constraints. Our proposed approach involves two edge-based distributed algorithms, differentiated by their access to players’ actions, whether it is full-decision information or partial-decision information. We establish the parameter range and demonstrate the convergence of both algorithms, showcasing their efficacy under local constant step-sizes. Additionally, we validate the effectiveness and advantages of these algorithms through two numerical experiments.

Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines.

Evolutionary Competition Multitasking Optimization with Online Resource Allocation for Endmemeber Extraction of Hyperspectral Images

Hyperspectral remote sensing images typically have mixed rather than pure pixels. Endmember extraction aims to find a group of endmembers to represent the original image. In fact, the amount of endmembers is not easily determined in the existing endmember extraction studies.It requires several separate and laborious runs in order to produce results for endmember extraction with varying numbers of endmembers. There is also a correlation between the individual runs, which should be taken into account to accelerate algorithm convergence and improve accuracy. In this paper, an evolutionary competition multitasking optimization method (CMTEE) is proposed to achieve endmember extraction. In the proposed method, endmember extraction problems with different numbers of endmembers are considered as a group of optimization tasks. Specially, these tasks are assumed to be competitive. Then, online resource allocation is employed to assign suitable computational resources to the considered tasks. Experiments on simulated and real hyperspectral datasets demonstrated the effectiveness of the proposed evolutionary competition multitasking optimization method for endmember extraction.

Simplified Algorithm for the Worldvolume HMC and the Generalized Thimble HMC

Abstract The Worldvolume Hybrid Monte Carlo method (WV-HMC method) is a reliable and versatile algorithm towards solving the sign problem. Like the tempered Lefschetz thimble method, this method removes the ergodicity problem inherent in algorithms based on Lefschetz thimbles. In addition to this advantage, the WV-HMC method significantly reduces the computational cost because one need not compute the Jacobian of deformation in generating configurations. A crucial step in this method is the RATTLE algorithm, where the Newton method is used at each molecular dynamics step to project a transported configuration onto a submanifold (worldvolume) in the complex space. In this paper, we simplify the RATTLE algorithm by employing a simplified Newton method (the fixed-point method) along with iterative solvers for orthogonal decompositions of vectors, and show that this algorithm further reduces the computational cost. We also apply this algorithm to the HMC algorithm for the generalized thimble method (GT-HMC method). We perform a numerical test for the convergence of the simplified RATTLE algorithm, and show that the convergence depends on the system size only weakly. The application of this simplified algorithm to various models will be reported in subsequent papers.

Bayesian model selection via mean-field variational approximation

Abstract This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference that allows latent variables and model misspecification. Concretely, we show a Bernstein–von Mises (BvM) theorem for the variational distribution from MF under possible model misspecification, which implies the distributional convergence of MF variational approximation to a normal distribution centring at the maximal likelihood estimator. Motivated by the BvM theorem, we propose a model selection criterion using the evidence lower bound (ELBO), and demonstrate that the model selected by ELBO tends to asymptotically agree with the one selected by the commonly used Bayesian information criterion (BIC) as the sample size tends to infinity. Compared to BIC, ELBO tends to incur smaller approximation error to the log-marginal likelihood (a.k.a. model evidence) due to a better dimension dependence and full incorporation of the prior information. Moreover, we show the geometric convergence of the coordinate ascent variational inference algorithm, which provides a practical guidance on how many iterations one typically needs to run when approximating the ELBO. These findings demonstrate that variational inference is capable of providing a computationally efficient alternative to conventional approaches in tasks beyond obtaining point estimates.

Multi-objective optimization of parameters design based on genetic algorithm in annulus aerated dual gradient drilling

The optimization of drilling parameters is crucial for resolving the drilling problems in low-pressure and leaky formations using the annulus aerated dual gradient drilling technology. However, the previous studies have mostly focused on engineering applications and wellbore fluid flow models, with less emphasis on parameter optimization. This paper combines the wellbore multiphase flow model with genetic algorithms for the first time, proposing a key parameter optimization method for annulus aerated dual gradient drilling based on genetic algorithms. The study investigates the impact of selection operators on the performance of genetic algorithms and compares genetic algorithms with PSO algorithm and SAA. The results indicate that the convergence and stability of genetic algorithms can be improved by enhancing the selection operators. Compared to the gas–liquid ratio parameter optimization method, the IRSGA optimization method reduces the cost coefficient by 36.46%. Through comparative analysis of different optimization methods, the IRSGA demonstrates over 95% accuracy in large-scale computations. The research findings contribute to the optimization of parameters design under low-cost conditions and are of significant importance for promoting the use of this technology to address the serious issue of lost circulation in drilling technology.

A Full-Newton Step Interior-Point Method for Weighted Quadratic Programming Based on the Algebraic Equivalent Transformation

In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm.

DNA Sequences Under Multiple Guanine-Cytosine (GC) Base Pairs Constraint.

DNA computing is a new computing method that has high efficiency in solving large-scale nonlinear and Non-deterministic Polynomial complete problems. The design of DNA sequences is an important step in DNA computing, and the quality of the DNA sequences directly affects the accuracy of DNA computing results. Efficiently designing high-quality DNA sequences is currently a significant challenge. In order to improve the efficiency of DNA sequence design, a sparrow evolutionary search algorithm (SESA) is proposed by us. It inherits the fast convergence of the sparrow search algorithm and avoids the situation that the sparrow search algorithm is prone to fall into a local optimum, which greatly improves the search performance of the algorithm on discrete numerical problems. In order to improve the quality of DNA sequence, a new constraint, multiple GC constraint, has been proposed in this paper. Simulated experiments in NUPACK show that this constraint can greatly improve the quality of the DNA sequences designed by us. Compared with previous results, our DNA sequences have better stability.

Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design.

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.