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Summary This article considers the problem of edge‐based event‐triggered output feedback control for linear multi‐agent systems (MASs) with state‐independent process and measurement noise under undirected communication topologies. The main breakthroughs are the design of distributed event‐triggered output feedback control strategy and the stochastic stability analysis. Toward this, first, according to Kalman filtering theory, An observer is contrasted to optimally estimate the state of each agent. Next, a novel edge‐based event‐triggered mechanism (EBETM) is designed to reduce the communication frequency among agents effectively, and a positive interval between events is enforced in EBETM, which can eliminate the Zeno behavior. Then, stability of the estimation error and the consensus error systems is analyzed, the execution error is estimated and the almost sure consensus is achieved. Finally, a numerical example is given to show that MASs achieves almost sure consensus and there is a positive interval between the events of all edges. [ABSTRACT FROM AUTHOR]

Stochastic proximal gradient descent (Prox-SGD) is a standard optimization algorithm for solving stochastic composite optimization problems in machine learning. However, the existing convergence rate analysis of Prox-SGD is mostly focused on convergence in expectation. To this end, we provide an almost sure convergence rate analysis of Prox-SGD in two optimization settings: convexity and strong convexity, showing that any implementation of the stochastic algorithm will converge with probability one. Specifically, we show that the average-iterates almost sure convergence rate of the function values for Prox-SGD is arbitrarily close to the optimal rate $ o(1/\sqrt {T}) $ o (1 / T) in the convex setting. For strongly convex objective functions, we obtain the almost sure convergence rate of the iterative sequence, which is also arbitrarily close to the optimal rate $ o(1/T) $ o (1 / T). Last but not least, we establish the more challenging last-iterate convergence rate of the function values on convex problems, which contrasts with existing results on convergence for a weighted average. [ABSTRACT FROM AUTHOR]

In this work, we establish the linear convergence estimate for the gradient descent involving the delay τ ∈ ℕ when the cost function is μ -strongly convex and L -smooth. This result improves upon the well-known estimates in [Y. Arjevani, O. Shamir and N. Srebro, A tight convergence analysis for stochastic gradient descent with delayed updates, Proc. Mach. Learn. Res. 117 (2020) 111–132; S. U. Stich and S. P. Karimireddy, The error-feedback framework: Better rates for SGD with delayed gradients and compressed updates, J. Mach. Learn. Res. 21(1) (2020) 9613–9648] in the sense that it is non-ergodic and is still established in spite of weaker constraint of cost function. Also, the range of learning rate η can be extended from η ≤ 1 / (1 0 L τ) to η ≤ 1 / (4 L τ) for τ = 1 and η ≤ 3 / (1 0 L τ) for τ ≥ 2 , where L > 0 is the Lipschitz continuity constant of the gradient of cost function. In a further research, we show the linear convergence of cost function under the Polyak–Łojasiewicz (PL) condition, for which the available choice of learning rate is further improved as η ≤ 9 / (1 0 L τ) for the large delay τ. The framework of the proof for this result is also extended to the stochastic gradient descent with time-varying delay under the PL condition. Finally, some numerical experiments are provided in order to confirm the reliability of the analyzed results. [ABSTRACT FROM AUTHOR]

Convergence provides clues to unveil the non-random nature of evolution. Intermediate paths toward convergence inform us of the stochasticity and the constraint of evolutionary processes. Although previous studies have suggested that substantial constraints exist in microevolutionary paths, it remains unclear whether macroevolutionary convergence follows stochastic or constrained paths. Here, we performed comparative genomics for hundreds of lactic acid bacteria (LAB) species, including clades showing a convergent gene repertoire and sharing fructose-rich habitats. By adopting phylogenetic comparative methods we showed that the genomic convergence of distinct fructophilic LAB (FLAB) lineages was caused by parallel losses of more than a hundred orthologs and the gene losses followed significantly similar orders. Our results further suggested that the loss of adhE, a key gene for phenotypic convergence to FLAB, follows a specific evolutionary path of domain architecture decay and amino acid substitutions in multiple LAB lineages sharing fructose-rich habitats. These findings unveiled the constrained evolutionary paths toward the convergence of free-living bacterial clades at the genomic and molecular levels. Using comparative genomics, the authors unveil constrained evolutionary paths both at genomic and molecular levels during convergent evolution of two distinct lactic acid bacteria lineages. [ABSTRACT FROM AUTHOR]

An optimal energy mix is a sine qua non for sustainable development. However, the global energy mix is sub-optimally dominated by fossils which endangers energy security and threatens the attainment of sustainable development. Understanding the convergence of energy series can assist the transition path to optimal energy mix and sustainable development. Thus, research on the convergence of several energy series has gained prominence in recent years. This study extends this important niche in the literature on the convergence of natural resources and environmental series by examining the convergence in energy diversification along several dimensions for a panel of 79 lower-middle, higher-middle, and high-income countries. As a departure from the existing studies, the study employs a novel methodology that allows abrupt or smooth changes through the Fourier approximation of smooth breaks, while including factor structures to test for the presence of unit roots in the relative energy diversification series. The results provide evidence of convergence of the energy diversification series in the majority of the considered countries, with 90% of the sample demonstrating convergence. A disaggregated country analysis was conducted and the findings show that 93% of the lower-middle-income countries are converging, while 95% of the upper-middle-income countries and 87% of the high-income countries are converging. Policy implications of the findings are also discussed. [ABSTRACT FROM AUTHOR]

Evolutionary multitask optimization (EMTO) has developed fast recently, and many algorithms have emerged that solve several different problems simultaneously through knowledge transfer. Most algorithms use a single search operator in their processing. However, different tasks have distinct characteristics, and a single operator is often inadequate to adapt to different stages of the same task. In this paper, we propose a multiple search operator selection strategy by adaptive probability allocation, named adaptive multi-operator selection (AMOS) to address EMTO that features rapid convergence of populations. It can automatically select the best multiple search operators based on the characteristics of specific tasks and different stages of evolution. The primary contributions of the proposed algorithm are as follows: (1) It combines the basic concepts of multi-operator integration and adaptive search operator selection to select the best multiple search operators for each task at different evolutionary stages; (2) It facilitates the knowledge transfer through different solving operators between tasks; (3) It can be flexibly embedded into various frameworks of general EMTO algorithms with good results. In the experiments, we validate the performance of AMOS on CEC2017 benchmark suite, CMTOPs benchmark suite, and real-world EMTO problems, and experimental results demonstrate the effectiveness and generality of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization of a class of nonlinear multiple neural networks (MNNs) with multi-delays was considered under a dynamic event-based mechanism. To achieve a more comprehensive synchronization outcome and mitigate the conservativeness of impulsive control due to predetermined time sequences, we integrated a dynamic event-triggered strategy. This approach formed a novel control framework for generalized MNNs, where impulsive inputs were applied only under specific conditions governed by event-triggering rules. Towards the above objectives, the impulsive jumping system, resulting from dynamic component, and matrix measure method were invoked to directly increase the computational simplicity and extensibility of the study. As the outcome, the synchronization criteria for the MNNs could be achieved, and the exponential convergence rate is resolved by considering both the generalized comparison principle regarding impulsive systems and the variable parameter formula. Moreover, Zeno-freeness of the achieved triggering regulation is ensured. Finally, two numerical examples confirmed the validity of the designed approach. [ABSTRACT FROM AUTHOR]

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow us to estimate the orders of the model. Theoretical considerations are validated using experimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behaviour of a family of random free-discontinuity energies E ε defined in a randomly perforated domain, as ε goes to zero. The functionals E ε model the energy associated to displacements of porous random materials that can develop cracks. To gain compactness for sequences of displacements with bounded energies, we need to overcome the lack of equi-coerciveness of the functionals. We do so by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The limit energy is then obtained in two steps. As a first step, we apply a general result of stochastic convergence of free-discontinuity functionals to a modified, coercive version of E ε . Then the effective volume and surface energy densities are identified by means of a careful limit procedure. [ABSTRACT FROM AUTHOR]

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavior of the oscillations, and to do this we use closed measures, a concept that complements the technique of asymptotic pseudotrajectories developed in this setting by Benaïm--Hofbauer--Sorin. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. Various cases are discussed, providing new insight into the oscillation and the stabilization phenomena. [ABSTRACT FROM AUTHOR]

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in several stages and involve various technological tools and various fields of mathematics. The activities can be useful for the instruction of pre-service and experienced mathematics teachers. [ABSTRACT FROM AUTHOR]

In this work, we have proposed a general manner to extend some two-parametric with-memory methods to obtain simple roots of nonlinear equations. Novel improved methods are two-step without memory and have two self-accelerator parameters that do not have additional evaluation. The methods have been compared with the nearest competitions in various numerical examples. Anyway, the theoretical order of convergence is verified. The basins of attraction of the suggested methods are presented and corresponded to explain their interpretation. [ABSTRACT FROM AUTHOR]

An analytical study of two different models of rectangular porous fins are investigated using a new approximate analytical method, the Ananthaswamy-Sivasankari method. The obtained results are compared with the numerical solution, which results in a very good agreement. The impacts of several physical parameters involved in the problem are interlined graphically. Fin efficiency and the heat transfer rate are also calculated and displayed. The result obtained by this method is in the most explicit and simple form. The convergence of the solution determined is more accurate as compared to various analytical and numerical methods. [ABSTRACT FROM AUTHOR]

This study aims to investigate a stochastic Volterra integral equation driven by fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). We employ the Wong-Zakai approximation to simplify this intricate problem, transforming the stochastic integral equation into an ordinary integral equation. Moreover, we consider the convergence and the rate of convergence of the Wong-Zakai approximation for this kind of equation. [ABSTRACT FROM AUTHOR]

Robust approach is a special scalarization method to deal with multiobjective optimization problems in the worst-case. In this paper, we propose a new non-monotone gradient type algorithm for solving unconstrained multiobjective optimization problems by the conjugate technique and the robust approach. The proposed method has a memory gradient property since the search direction is constructed by using the current descent direction and the past multi-step iterative descent directions. For this, the search direction is called a memory gradient search direction. The step-size is computed by the non-monotone linear search. A lower bound of the stepsize is presented under some mild conditions. Then the iterative sequence generated by the proposed method is proved to be convergent to a Pareto critical point of the multiobjective optimization problem under some mild conditions. Numerical experiments are reported to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inexact projected gradient method equipped with a nonmonotone line search rule for smooth constrained multiobjective optimization. In this method, a new nonmonotone line search technique proposed here is employed and the relative errors on the search direction is admitted. We demonstrate that this method is well-defined. Then, we prove that each accumulation point of the sequence generated by this method is Pareto stationary and analyze the convergence rate of the algorithm. When the objective function is convex, the convergence of the sequence to a weak Pareto optimal point of the problem is established. [ABSTRACT FROM AUTHOR]

The co-infection of HIV and COVID-19 is a pressing health concern, carrying substantial potential consequences. This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 coinfection, a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches. Here, we introduce an innovative mathematical model grounded in Caputo fractional order differential equations, specifically designed to encapsulate the intricate dynamics of co-infection. This model encompasses multiple critical facets: the transmission dynamics of both HIV and COVID-19, the host’s immune responses, and the influence of treatment interventions. Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics. To tackle the fractional order model, we employ the Laplace-Adomian decomposition method, a potent mathematical tool for approximating solutions in fractional order differential equations. Utilizing this technique, we simulate the intricate interactions between these variables, yielding profound insights into the propagation of co-infection. Notably, we identify pivotal contributors to its advancement. In addition, we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method. This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions. Our findings hold significant implications for the formulation of effective control strategies. Policymakers, healthcare professionals, and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection. [ABSTRACT FROM AUTHOR]

This paper examines the concepts and practical applications of the spanning tree protocol (STP). It also covers per-VLAN spanning tree (PVST), multiple spanning tree (MST), and rapid STP (RSTP). Moreover, practical scenarios are presented to help the reader understand the concepts and implementations of these protocols. This study analyzes protocols using seven metrics. All protocols have been evaluated using these metrics in both small and big topology scenarios to obtain the best results. In addition, all metrics are mentioned in the introduction chapter, and the way used to apply tests on the metrics is described in the methodology chapter. Based on the experiments, different STPs performance are compared, including STP, RSTP, PVST, and MST. In summary, findings show that STP is easy to use and performs well overall, but it consistently has high latency issues. RSTP is suitable for small networks and has quick convergence, but it cannot handle as much load as STP. PVST performed the best in the experiments, as it demonstrated high scalability and the ability to handle a lot of pressure, although it requires strong hardware. However, MST did not perform as well as expected, as it struggled with delay problems and high jitter. In conclusion, it is recommended to use RSTP for simple networks that require fast convergence with dependable delay and capacity, or STP for networks that require good scaling and bandwidth. PVST is an excellent option for those who can afford high-performance hardware, while MST is suitable for simple networks or those with outdated hardware. [ABSTRACT FROM AUTHOR]

The Lowest Unique Positive Integer game, a.k.a. Limbo, is among the simplest games that can be played by any number of players and has a nontrivial strategic component. Players independently pick positive integers, and the winner is the player that picks the smallest number nobody else picks. The Nash equilibrium for this game is a mixed strategy, (p (1) , p (2) , ...) , where p(k) is the probability you pick k. A recursion for the Nash equilibrium has been previously worked out in the case where the number of players is Poisson distributed, an assumption that can be justified when there is a large pool of potential players. Here, we summarize previous results and prove that as the (expected) number of players, n, goes to infinity, a properly scaled version of the Nash equilibrium random variable converges in distribution to a Unif(0, 1) random variable. The result implies that for large n, players should choose a number uniformly between 1 and ϕ n ∼ O (n / ln (n)) . Convergence to the uniform is rather slow, so we also investigate a continuous analog of the Nash equilibrium using a differential equation derived from the recursion. The resulting approximation is unexpectedly accurate and is interesting in its own right. Studying the differential equation yields some useful analytical results, including a precise expression for ϕ n , and efficient ways to sample from the continuous approximation. [ABSTRACT FROM AUTHOR]

The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study McKean–Vlasov stochastic differential equations driven by Lévy processes. Firstly, under the non-Lipschitz condition which include classical Lipschitz conditions as special cases, we establish the existence and uniqueness for solutions of McKean–Vlasov stochastic differential equations using Carathéodory approximation. Then under certain averaging conditions, we establish a stochastic averaging principle for McKean–Vlasov stochastic differential equations driven by Lévy processes. We find that the solutions to stochastic systems concerned with Lévy noise can be approximated by solutions to averaged McKean–Vlasov stochastic differential equations driven by Lévy processes in the sense of convergence in p th moment. [ABSTRACT FROM AUTHOR]

Copyright of Informacije MIDEM: Journal of Microelectronics, Electronic Components & Materials is the property of MIDEM Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper studies the analytical solution to the Fractional Differential Equations (FDEs) under uncertainty. Fuzzy differential equations are one of the emerging topics in the present era of research, where we have found an effective combination of FDEs with fuzziness. The Homotopy Analysis Transform Method (HATM) with the Caputo fractional derivative is applied in this work to find the analytical fuzzy solution of two fuzzy FDEs. One of the interesting parts of this study is that we have found upper and lower fuzzy solutions for both fuzzy FDEs. The different graphical representations that have been presented for both examples show that there is a symmetry relation between the upper and lower-cut fuzzy solutions. In this method, the region and rate of convergence of the solution series are controlled by the auxiliary parameter r-cut. This paper shows that the proposed method is reliable and efficient in determining the fuzzy solutions of the FDEs in applied mathematics and engineering [ABSTRACT FROM AUTHOR]

Copyright of Journal of Education & Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the study done here regarding the theory of summability, we introduce some new concepts in fuzzy normed spaces. First, at the beginning of the original part of our study, we define the lacunary invariant statistical convergence. Then, we examine some characteristic features like uniqueness, linearity of this new notion and give its important relation with pre-given concepts. [ABSTRACT FROM AUTHOR]

The conjugate gradient method plays a very important role in several fields, to solve problems of large sizes. To improve the efficiency of this method, a lot of works have been done; in this paper we propose a new modification of PRP method to solve a large scale unconstrained optimization problems in relation with strong Wolf Powell Line Search property, when the latter was used under some conditions, a global convergence result was proved. In comparison with other known methods the efficiency of this method proved that it is better in the number of iterations and in time on 90 proposed problems by use of Matlab. [ABSTRACT FROM AUTHOR]

In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q -symmetric starlike and q -symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q -analogue Salagean integral operator, the p -valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p -valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ , q -neighborhoods for p -valent functions are defined. In relation to symmetric δ , q -neighborhoods of q -symmetric p -valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q -symmetric inequalities of analytic functions with negative coefficients is also provided. [ABSTRACT FROM AUTHOR]

A pressure-robust stabilizer-free weak Galerkin (WG) finite element method has been defined for the Stokes equations on triangular and tetrahedral meshes. We have obtained pressure-independent error estimates for the velocity without any velocity reconstruction. The optimal-order convergence for the velocity of the WG approximation has been proved for the L 2 norm and the H 1 norm. The optimal-order error convergence has been proved for the pressure in the L 2 norm. The theory has been validated by performing some numerical tests on triangular and tetrahedral meshes. [ABSTRACT FROM AUTHOR]

Meta-learning is a pivotal and potentially influential machine learning approach to solve challenging problems in reinforcement learning. However, the costly hyper-parameter tuning for training stability of meta-learning is a known shortcoming and currently a hotspot of research. This paper addresses this shortcoming by introducing an online and easily trainable hyper-parameter optimization approach, called Meta Parameters Learning via Meta-Learning (MPML), to combine online hyper-parameter adjustment scheme into meta-learning algorithm, which reduces the need to tune hyper-parameters. Specifically, a basic learning rate for each training task is put forward. Besides, the proposed algorithm dynamically adapts multiple basic learning rate and a shared meta-learning rate through conducting gradient descent alongside the initial optimization steps. In addition, the sensitivity with respect to hyper-parameter choices in the proposed approach are also discussed compared with model-agnostic meta-learning method. The experimental results on reinforcement learning problems demonstrate MPML algorithm is easy to implement and delivers more highly competitive performance than existing meta-learning methods on a diverse set of challenging control tasks. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

The level-set subdifferential error bound (LSEB) is weaker than the Kurdyka-Łojasiewicz (KL) property and can replace it to establish linear convergence for various first-order algorithms. In this paper, we mainly study the behaviour of the level-set subdifferential error bound via Moreau envelopes under suitable assumptions. We provide an example that the Moreau envelope does not have the KL property but has the LSEB when the original function does not satisfy the KL property but only the LSEB. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients. We establish the convergence of the proposed algorithm under the KurdykaŁojasiewicz assumption by constructing a suitable energy function with a non-increasing property. As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems. Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the quasi-convex feasibility problem (QFP), which is to find a common point of a family of sublevel sets of quasi-convex functions. By employing the Bregman projection mapping, we propose a unified framework of Bregman quasi-subgradient methods for solving the QFP. This paper is contributed to establish the convergence theory, including the global convergence, iteration complexity, and convergence rates, of the Bregman quasi-subgradient methods with several general control schemes, including the a-most violated constraints control and the s-intermittent control. Moreover, we introduce a notion of the Hölder-type bounded error bound property relative to the Bregman distance for the QFP, and use it to establish the linear (or sublinear) convergence rates for Bregman quasi-subgradient methods to a feasible solution of the QFP. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of composite optimization problems, whose objective function is the summation of a bunch of nonsmooth nonconvex loss functions and a cardinality regularizer. Firstly we investigate the optimality condition of these problems and then suggest a stochastic proximal subgradient method (SPSG) to solve them. Then we establish the almost surely subsequence convergence of SPSG under mild assumptions. We emphasize that these assumptions are satisfied by a wide range of problems arising from training neural networks. Furthermore, we conduct preliminary numerical experiments to demonstrate the effectiveness and efficiency of SPSG in solving this class of problems. [ABSTRACT FROM AUTHOR]

Reducing multidimensional relative poverty is one of the important issues in the current global poverty governance field. This article takes 12 ethnic regions in China as the research object and constructs a multidimensional relative poverty measurement system. The calculated multidimensional relative poverty index is decomposed according to provinces, cities, dimensions, and indicators. Then, the Dagum Gini coefficient and convergence analysis are used to analyze spatiotemporal heterogeneity and convergence characteristics. The results show that the multi-dimensional relative poverty situation of various provinces in ethnic minority areas has improved from 2012 to 2021, among which Tibet province is the most serious and Shaanxi is the best. According to the analysis of convergence, it was observed that there is no σ-convergence of multidimensional relative poverty in ethnic areas in general, and there is absolute β-convergence in general and in the southwest and northwest regions, and there is no absolute β-convergence in the northeast region. Based on this, policy recommendations for reducing multidimensional relative poverty are proposed at the end of the article. Compared with previous studies, this article focuses on ethnic regions that are easily overlooked. Starting from the dimensions of economy, social development, and ecological environment, the poverty measurement system has been enriched. [ABSTRACT FROM AUTHOR]

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system. [ABSTRACT FROM AUTHOR]

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization (SDFO) which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple stochastic direct-search and trust-region methods for the optimization of a potentially nonsmooth function whose values can only be estimated via stochastic observations. For trial points to be accepted, these algorithms require the estimated function values to yield a sufficient decrease measured in terms of a power larger than 1 of the algoritmic stepsize. Our new tail bound condition is precisely imposed on the reduction estimate used to achieve such a sufficient decrease. This condition allows us to select the stepsize power used for sufficient decrease in such a way that the number of samples needed per iteration is reduced. In previous works, the number of samples necessary for global convergence at every iteration k of this type of algorithm was O(\Delta 4 k), where Delta k is the stepsize or trust-region radius. However, using the new tail bound condition, and under mild assumptions on the noise, one can prove that such a number of samples is only O(\Delta 2 varepsilon k ), where varepsilon > 0 can be made arbitrarily small by selecting the power of the stepsize in the sufficient decrease test arbitrarily close to 1. In the common random number generator setting, a further improvement by a factor of Delta 2 k can be obtained. The global convergence properties of the stochastic direct-search and trust-region algorithms are established under the new tail bound condition. [ABSTRACT FROM AUTHOR]

Majorization–minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the objective function so that along the iterations the objective value decreases. We present a stochastic higher-order algorithmic framework for minimizing the average of a very large number of sufficiently smooth functions. Our stochastic framework is based on the notion of stochastic higher-order upper bound approximations of the finite-sum objective function and minibatching. We derive convergence results for nonconvex and convex optimization problems when the higher-order approximation of the objective function yields an error that is p times differentiable and has Lipschitz continuous p derivative. More precisely, for general nonconvex problems we present asymptotic stationary point guarantees and under Kurdyka–Lojasiewicz property we derive local convergence rates ranging from sublinear to linear. For convex problems with uniformly convex objective function, we derive local (super)linear convergence results for our algorithm. Compared to existing stochastic (first-order) methods, our algorithm adapts to the problem's curvature and allows using any batch size. Preliminary numerical tests support the effectiveness of our algorithmic framework. [ABSTRACT FROM AUTHOR]

Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model. A weighted least-square approximation problem of the relaxation modulus by the fractional Maxwell model is considered when only the time measurements of the relaxation modulus corrupted by additive noises are accessible for identification. This study was dedicated to the determination of the model, optimal in the sense of the integral square weighted model quality index, which does not depend on the particular sampling points applied in the stress relaxation experiment. It is proved that even when the real description of the material relaxation modulus is entirely unknown, the optimal fractional Maxwell model parameters can be recovered from the relaxation modulus measurements recorded for sampling time points selected randomly according to respective randomization. The identified model is a strongly consistent estimate of the desired optimal model. The exponential convergence rate is demonstrated both by the stochastic convergence analysis and by the numerical studies. A simple scheme for the optimal model identification is given. Numerical studies are presented for the materials described by the short relaxation times of the unimodal Gauss-like relaxation spectrum and the long relaxation times of the Baumgaertel, Schausberger and Winter spectrum. These studies have shown that the appropriate randomization introduced in the selection of sampling points guarantees that the sequence of the optimal fractional Maxwell model parameters asymptotically converge to parameters independent of these sampling points. The robustness of the identified model to the measurement disturbances was demonstrated by analytical analysis and numerical studies. [ABSTRACT FROM AUTHOR]

This manuscript puts forward two new generalized families of Jarratt's iterative schemes for deciding the solution of scalar and systems of nonlinear equations. The schemes involve weight functions that are based on bi-variate rational approximation polynomial of degree two in both its numerator and denominator. The convergence study conducted on the schemes, indicated that they have convergence order (CO) four in scalar space and retain the same number of CO in vector space. The numerical experiments conducted on the schemes when used to decide the solutions of some real-life nonlinear models show that they are good challengers of some well-known and robust existing iterative schemes. [ABSTRACT FROM AUTHOR]

In this article, we explore the discontinuous Galerkin finite element method for two-parametric singularly perturbed convection-diffusion problems with a discontinuous source term. Due to the discontinuity in the source term, the problem typically shows a weak interior layer. Also, the presence of multiple perturbation parameters in the problem causes boundary layers on both sides of the boundary. In this work, we develop the nonsymmetric discontinuous Galerkin finite element method with interior penalties to handle the layer phenomenon. With the use of a typical Shishkin mesh, the domain is discretized, and a uniform error estimate is obtained. Numerical experiments are conducted to validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

The paper proposes an iterative method for solving a variational inclusion with the sum of two operators in a Hilbert space. The method can be considered as a combination of the proximal contraction method, the regularization method, and the multi-step inertial technique. Theorem of strong convergence is established under mild conditions imposed on cost operators and control parameters. [ABSTRACT FROM AUTHOR]

Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Progam. 1992] has inspired intensive attention in analyzing its theoretical convergence properties. This paper is devoted to the linear convergence rate of the semi-proximal GADMM (sPGADMM) for solving linearly constrained convex composite optimization problems. The semi-proximal terms contained in each subproblem possess the abilities of handling with multi-block problems efficiently. We initially present some important inequalities for the sequence generated by the sPGADMM, and then establish the local linear convergence rate under the assumption of calmness. As a by-product, the global convergence property is also discussed. [ABSTRACT FROM AUTHOR]

This paper presents numerical methods for solving the one-dimensional fractional reaction-diffusion equation with the fractional Caputo derivative. The proposed methods are based on transformation of the fractional differential equation to an equivalent form of a integro-differential equation. The paper proposes an improvement of the existing implicit method, and a new explicit method. Stability and convergence tests of the methods were also conducted. [ABSTRACT FROM AUTHOR]

For a Dirichlet series of form F(s) = exp{sλ1} + P+∞ k=2 fk exp{sλk} (1) abcolutely convergent in the half-plane Π0 = {s: Re s < 0} new sufficient conditions for the close-to-pseudoconvexity are found and the obtained result is applied to studying of solutions linear differential equations of second order with exponential coefficients. In particular, are proved the following statements: 1) Let λk = λk-1 + λ1 and fk > 0 for all k ≥ 2. If 1 ≤ λ2f2/λ1 ≤ 2 and λkfk-λk+1fk+1 ↘ q ≥ 0 as k → +∞ then function of form (1) is close-to-pseudoconvex in Π0 (Theorem 3). This theorem complements Alexander's criterion obtained for power series. 2) If either -h2 ≤ γ ≤ 0 or γ = h2 then differential equation (1-ehs)2w′′-h(1-e2hs)w′+γe2hs = 0 (h > 0, γ ∈ R) has a solution w = F of form (1) with the exponents λk = kh and the the abscissa of absolute convergence σa = 0 that is close-to-pseudoconvex in Π0 (Theorem 4). [ABSTRACT FROM AUTHOR]

Let λ = (λn)n∈N0 be a non-negative sequence increasing to +∞, τ (λ) = limn→∞(ln n/λn), and D0(λ) be the class of all Dirichlet series of the form F(s) = P∞ n=0 an(F)esλn absolutely convergent in the half-plane Re s < 0 with an(F) ̸= 0 for at least one integer n ≥ 0. Also, let α be a continuous function on [x0,+∞) increasing to +∞, β be a continuous function on [a, 0) such that β(σ) → +∞ as σ ↑ 0, and γ be a continuous positive function on [b, 0). In the article, we investigate the growth of a Dirichlet series F ∈ D0(λ) depending on the behavior of the sequence (|an(F)|) in terms of its α, β, γ-orders determined by the equalities... where μ(σ) = max{|an(F)|eσλn: n ≥ 0} and M(σ) = sup{|F(s)|: Re s = σ} are the maximal term and the supremum modulus of the series F, respectively. In particular, if for every fixed t > 0 we have α(tx) ∼ α(x) as x → +∞, β(tσ) ∼ t-ρβ(σ) as σ ↑ 0 for some fixed ρ > 0, 0 < limσ↑0 γ(tσ)/γ(σ) ≤ limσ↑0 γ(tσ)/γ(σ) < +∞, Φ(σ) = α-1(β(σ))/γ(σ) for all σ ∈ [σ0, 0), eΦ(x) = max{xσ -Φ(σ): σ ∈ [σ0, 0)} for all x ∈ R, and ΔΦ(λ) = limn→∞(-ln n/eΦ(λn)), then: (a) for each Dirichlet series F ∈ D0(λ) we have... (b) if τ (λ) > 0, then for each p0 ∈ [0,+∞] and any positive function Ψ on [c, 0) there exists a Dirichlet series F ∈ D0(λ) such that R∗ α,β,γ(F) = p0 and M(σ, F) ≥ Ψ(σ) for all σ ∈ [σ0, 0); (c) if τ (λ) = 0, then (Rα,β,γ(F))1/ρ ≤ (R∗ α,β,γ(F))1/ρ + ΔΦ(λ) for every Dirichlet series F ∈ D0(λ); (d) if τ (λ) = 0, then for each p0 ∈ [0,+∞] there exists a Dirichlet series F ∈ D0(λ) such that R∗ α,β,γ(F) = p0 and (Rα,β,γ(F))1/ρ = (R∗ α,β,γ(F))1/ρ + ΔΦ(λ). [ABSTRACT FROM AUTHOR]

Optimization methods are widely used in various fields to find the best possible solution to a given problem through the minimization or maximization of an objective function while adhering to specific constraints. In this paper, we present a new optimization algorithm, called WOADD, which was designed to handle the challenges of constrained optimization problems that involve dependent data. Unlike traditional algorithms that struggle with data dependencies and valid range constraints, WOADD uses a unique normalization process and a dynamic updating mechanism that accurately considers the interdependencies among features. By calculating a scaling parameter to navigate within feasible regions, WOADD adjusts its search strategy to ensure the preservation of data dependencies and adherence to constraints, ultimately leading to more efficient and precise optimization outcomes. Our extensive experimental analysis, which compared WOADD against other swarm optimization methods using a suite of benchmark functions, demonstrates its superior performance in terms of faster convergence rates, improved solution quality, and enhanced determinism in outcomes. [ABSTRACT FROM AUTHOR]