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In machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit asymptotic convergence. In order to ensure that the optimization problem converges to the optimal solution within the prescribed time, a novel prescribed-time convergence acceleration algorithm with time rescaling is presented in this paper. Two prescribed-time acceleration algorithms are constructed by introducing time rescaling, and the acceleration algorithms are used to solve unconstrained optimization problems and optimization problems containing equation constraints. Some important theorems are given, and the convergence of the acceleration algorithms is proven using the Lyapunov function method. Finally, we provide numerical simulations to verify the effectiveness and rationality of our theoretical results. [ABSTRACT FROM AUTHOR]

More and more attention has been paid to ships with a DC power grid. State-of-charge (SOC) estimation is a pivotal and challenging assignment for lithium-ion batteries in such ships. However, the precision of SOC estimation is strongly connected with the system parameters. To better identify these parameters in lithium-ion batteries, a differential evolution (DE) algorithm was introduced into this paper as the optimizer. Initially, a first-order RC equivalent circuit model (ECM) was created to characterize the battery's dynamic behavior. Following this, to estimate open-circuit voltage (OCV) throughout the entire dynamic process, a math model of optimization was established to minimize inaccuracies between the real and estimated terminal voltages. Moreover, estimated SOC values were obtained through OCV-SOC mappings and were contrasted against the true SOC values. The findings manifested the efficacy of the presented structure and technique in comparison with various frequently-cited DE variants. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the enhancement of global navigation satellite system (GNSS) adaptive acquisition using metaheuristic optimization techniques is proposed. The principal goal of this work is to optimize the cell averaging constant false alarm rate (CA‐CFAR) thresholding in Rayleigh fading channels. In GNSS acquisition, pilot and data blocks may have different thresholds. Thus, the optimization will focus on two scaling factors (T1 and T2). Two fusion rules have been used here ("AND" and "OR"). Due to their performances in different optimization problems, metaheuristics have been chosen to be our tool for solving this kind of problem. Simulation results show that the optimized thresholds have an important influence on the performance of the acquisition system. [ABSTRACT FROM AUTHOR]

In this article, we work on vector optimization problems in linear topological spaces. Our vector optimization problems have weakened convex inequality constraints and weakened affine equality constraints. Our inequalities are given by partial orders that are induced by pointed convex cones. We prove a Farkas–Minkowski-type theorem of alternative and obtain some optimality conditions through the discussions of vector saddle points and scalar saddle points.

The paper proposes an approach to solving the inverse epidemiological problem, written in terms of the "mean-field" theory. Finding the coefficients of an epidemiological SIR mean-field model is reduced to solving an optimization problem, for the solution of which only zero-order methods can be used. An algorithm for the solution of the inverse coefficient problem is proposed. Computational experiments were carried out to compare the obtained solutions with respect to synthetic and real data. The results of computational experiments have shown the efficiency of this approach. Ways to further improve the approach have also been determined. [ABSTRACT FROM AUTHOR]

Given a directed graph G = (V , A) , we tackle the Minimum Feedback Arc Set (MFAS) Problem by designing an efficient algorithm to search for minimal and stable Feedback Arc Sets, i.e. such that none of the arcs can be reintroduced in the graph without disrupting acyclicity and such that for each vertex the number of eliminated outgoing (resp. incoming) arcs is not bigger than the number of remaining incoming (resp. outgoing) arcs. Our algorithm has a good polynomial upper bound and can therefore be applied even on large graphs. We also introduce an algorithm to generate strongly connected graphs with a known upper bound on their feedback arc set, and on such graphs we test our algorithm. [ABSTRACT FROM AUTHOR]

This paper studies some results on solutions associated with interval-valued optimal control problems driven by generalized invariant convex (for short, invex) functionals. Necessary conditions of optimality are stated for the considered optimization problem. Also, the sufficiency of the necessary optimality conditions is investigated. Moreover, various duality relationships between the dual models and the primal optimization problem are deliberated. [ABSTRACT FROM AUTHOR]

This paper is devoted to an inverse problem for a nonlinear parabolic equation related to brain tumor dynamics. After reformulating the inverse problem as a minimization problem, we prove the existence and stability of the solution to the minimization problem. Based on the Fréchet differentiability of the objective (cost) functional, we develop an efficient iterative procedure for the numerical solution to the minimization problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent. [ABSTRACT FROM AUTHOR]

We consider a mathematical model which describes the equilibrium of two elastic membranes fixed on their boundary and attached to an adhesive body, say a glue. The variational formulation of the model is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove a convergence result, for which we provide the corresponding mechanical interpretation. Next, we consider two associated optimization problems for which we provide existence results. Finally, we the present numerical simulation which validates our convergence result. We end this paper with some concluding remarks and an Appendix, in which we present the preliminary material needed in this paper. [ABSTRACT FROM AUTHOR]

A smart grid is designed to enable the massive deployment and efficient use of distributed energy resources, including distributed photovoltaics (DPV). Due to the large number, wide distribution, and insufficient monitoring information of DPV stations, the pressure to maintain them has increased rapidly. Furthermore, based on reports in the relevant literature, there is still a lack of efficient large-scale maintenance strategies for DPV stations at present, leading to the high maintenance costs and overall low efficiency of DPV stations. Therefore, this paper proposes a maintenance period decision model and an areal maintenance strategy. The implementation steps of the method are as follows: firstly, based on the reliability model and dust accumulation model of the DPV components, the maintenance period decision model is established for different numbers of DPV stations and different driving distances; secondly, the optimal maintenance period is determined by using the Monte Carlo method to calculate the average economic benefits of daily maintenance during different periods; then, an areal maintenance strategy is proposed to classify all the DPV stations into different areas optimally, where each area is maintained to reach the overall economic optimum for the DPV stations; finally, the validity and rationality of this strategy are verified with the case study of the DPV poverty alleviation project in Badong County, Hubei Province. The results indicate that compared with an independent maintenance strategy, the proposed strategy can decrease the maintenance cost by 10.38% per year, which will help promote the construction of the smart grid and the development of sustainable cities. The results prove that the method proposed in this paper can effectively reduce maintenance costs and improve maintenance efficiency. [ABSTRACT FROM AUTHOR]

In this paper, based on the framework of the supplementary variable method, we present two classes of high-order, linearized, structure-preserving algorithms for simulating the regularized long-wave equation. The suggested schemes are as accurate and efficient as the recently proposed schemes in Jiang et al. (2022) [20] , but share the nice features in two folds: (i) the first type of schemes conserves the original energy conservation, as opposed to a modified quadratic energy in [20] ; (ii) the second type of schemes fills the gap of [20] by constructing high-order linear algorithms that preserve both two invariants of mass and momentum. We discretize the SVM systems by employing the algebraically stable Runge-Kutta method together with the prediction-correction technique in time and the Fourier pseudo-spectral method in space. The implementation benefits from solving the optimization problems subject to PDE constraints. Numerical examples and some comparisons are provided to show the effectiveness, accuracy and performance of the proposed schemes. [ABSTRACT FROM AUTHOR]

Near-field (NF) integrated sensing and communication (ISAC) has the potential to revolutionize future wireless networks. It enables simultaneous communication and sensing operations on the same radio frequency (RF) resources using a shared hardware platform, maximizing resource utilization. NF-ISAC systems can improve communication and sensing performance compared to traditional far-field (FF) ISAC systems by exploiting the unique propagation characteristics of NF spherical waves with an additional distance dimension. Despite its potential, NF-ISAC research is still in its early stages, and a comprehensive survey of the technology is lacking. This paper systematically explores NF-ISAC technology, providing an in-depth analysis of both NF and FF systems, their applicability in various scenarios, and different channel models. It highlights the advantages and philosophies of ISAC, examining both narrow-band and wide-band NF-ISAC systems. Case studies and simulations offer deeper insights into NF-ISAC design philosophies. Additionally, the paper reviews the existing NF-ISAC literature, methodologies, potentials, and conclusions, and discusses future research areas, challenges, and applications. [ABSTRACT FROM AUTHOR]

In this article, the authors present some results related to the search for an optimal solution to the optimization problem of managing an economic system with a finite number of interconnected institutions that are influenced by an external “regulator”. The regulator is interested in the fruitful interaction of all structures; it manages the system by setting appropriate priorities. The optimization problem comes down to finding the maximum point of the objective function of the regulator (optimizer). The paper presents an analytical solution to the problem and derives formulas for finding the maximum point of the objective function for the case of a finite number of deterministic priorities. [ABSTRACT FROM AUTHOR]

A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the L 1 norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem to the finite-dimensional optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we studied the AA-iterative algorithm for finding fixed points of the class of nonlinear generalized (α, β)-nonexpansive mappings. First, we proved weak convergence and then proved several strong convergence results of the scheme in a ground setting of uniformly convex Banach spaces. We gave a few numerical examples of generalized (α, β)-nonexpansive mappings to illustrate the major outcomes. One example was constructed over a subset of a real line while the other one was on the two dimensional space with a taxicab norm. We considered both these examples in our numerical computations to show that our iterative algorithm was more effective in the rate of convergence corresponding to other fixed point algorithms of the literature. Some 2D and 3D graphs were obtained that supported graphically our results and claims. As applications of our major results, we solved a class of fractional differential equations, 2D Voltera differential equation, and a convex minimization problem. Our findings improved and extended the corresponding results of the current literature [ABSTRACT FROM AUTHOR]

A novel approach is proposed for designing control strategies for time-varying cyber–physical systems (CPSs) with unknown dynamics, eliminating the need for system identification. Combining with the dynamic-triggered strategies (DTSs), the closed-loop system is parameterized using matrices that are depended on data obtained from a collection of input-state trajectories gathered offline. Additionally, the problem of data-driven optimization control is elegantly resolved through the utilization of classical linear quadratic regulator (LQR) technology, showcasing a remarkable innovation by obviating the necessity for the specific mathematical model of CPSs proposed in this paper. A numerical illustration is provided to illustrate these findings.

Getting around in modern cities has become a daily puzzle for both residents and travelers. As cities increasingly evolve into complex hubs of innovation and development, the demand for efficient transportation solutions has never been higher. In the multifaceted field of urban transportation, cost-effective and efficient mobility remains a high priority. This paper looks at how cities are planning better ways for people to travel and move within the growing scope of multimodal transportation, a paradigm shift beyond traditional single-mode transit systems. Our approach to improving urban transport revolves around a few key principles: integration, innovation, and collaboration. Integration means bringing together different modes of transportation – like buses, trains, bikes, and even new technologies like ride-sharing services to make it easier for people to switch between them. This transformative approach not only aims to reduce congestion and reduce environmental footprints but also prioritizes user experience while ensuring a harmonious blend of convenience, sustainability, and accessibility. We use new technology and ideas to ensure that travel is easy, quick, and good for the environment. Looking at new trends and examples from around the world, this overview shows how cities are shaping a better future for everyone's daily commute. In this paper, we use Lingo software to solve a numerical example related to multi-modal transportation, demonstrating practical solutions for real-world implementation. Through innovation, we can find creative solutions to urban transportation challenges. Additionally, public transportation enhancements, such as the introduction of synchronized bus routes and electric vehicle charging stations, underline the commitment to sustainability and inclusivity. In the dynamic urban transportation landscape, cities will revolutionize our approach to providing cost-effective and efficient mobility solutions.

Abstract In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.

In this paper, we studied the AA-iterative algorithm for finding fixed points of the class of nonlinear generalized $ (\alpha, \beta) $-nonexpansive mappings. First, we proved weak convergence and then proved several strong convergence results of the scheme in a ground setting of uniformly convex Banach spaces. We gave a few numerical examples of generalized $ (\alpha, \beta) $-nonexpansive mappings to illustrate the major outcomes. One example was constructed over a subset of a real line while the other one was on the two dimensional space with a taxicab norm. We considered both these examples in our numerical computations to show that our iterative algorithm was more effective in the rate of convergence corresponding to other fixed point algorithms of the literature. Some 2D and 3D graphs were obtained that supported graphically our results and claims. As applications of our major results, we solved a class of fractional differential equations, 2D Voltera differential equation, and a convex minimization problem. Our findings improved and extended the corresponding results of the current literature.

In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples. [ABSTRACT FROM AUTHOR]

The question "How does it work" has motivated many scientists. Through the study of natural phenomena and behaviors, many intelligence algorithms have been proposed to solve various optimization problems. This paper aims to offer an informative guide for researchers who are interested in tackling optimization problems with intelligence algorithms. First, a special neural network was comprehensively discussed, and it was called a zeroing neural network (ZNN). It is especially intended for solving time-varying optimization problems, including origin, basic principles, operation mechanism, model variants, and applications. This paper presents a new classification method based on the performance index of ZNNs. Then, two classic bio-inspired algorithms, a genetic algorithm and a particle swarm algorithm, are outlined as representatives, including their origin, design process, basic principles, and applications. Finally, to emphasize the applicability of intelligence algorithms, three practical domains are introduced, including gene feature extraction, intelligence communication, and the image process. [ABSTRACT FROM AUTHOR]

The rapid increase in the number of computing intensive tasks has led to an overload of SMD (Smart Mobile Devices) computing tasks. By using MEC(Mobile Edge Computing Servers) and idle ED (Edge Devices) in the network, SMD with limited computing power can offload computing tasks to MEC and ED collaboration, and enhance system security based on the DPoR (Delegated Proof of Reputation) consensus mechanism. This study proposes a blockchain mobile edge computing offloading model based on BS AFSA (Bird Swarm Artificial Fish Swarm Algorithm), which transforms the task offloading problem into an optimization objective function to reduce the computational overhead. The improved BS AFSA is used to optimize the task delay and energy consumption, and the behavior parameters in the algorithm are constructed and the crowding factor is improved to elevate the local search accuracy in the later iteration. The simulation results show that compared with other benchmark algorithms, the proposed algorithm reduces the possibility of falling into local optimum and effectively reduces the total system cost of the joint offloading scheme. [ABSTRACT FROM AUTHOR]

We propose a method to control the motion of a capsule endoscope (CE) in the stomach utilizing either a single external permanent magnet (EPM) or dual EPMs to extend the examination of the upper gastrointestinal tract. When utilizing the conventional magnetic navigational system (MNS) with a single EPM to generate tilting and rotational motions of the CE, undesired translational motion of the CE may prevent accurate examination. We analyzed the motion of the CE by calculating the magnetic torque and magnetic force applied to the CE using the point-dipole approximation model. Using the proposed model, we propose a method to determine the optimal position and orientation of the EPM to generate tilting and rotational motions without undesired translational motion of the CE. Furthermore, we optimized the weight of dual EPMs to develop a lightweight MNS. We prototyped the proposed MNS and experimentally verified that the developed MNS can generate tilting and rotational motions of the CE without any translational motion. [ABSTRACT FROM AUTHOR]

Chebyshev polynomials of the first kind are applied to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on an interval is solved, and its approximate properties on Holder classes H1 are analyzed. An exact equality is obtained for the deviation of Hölder class functions from the generalized Chebyshev–Poisson integral. [ABSTRACT FROM AUTHOR]

As the real estate industry expands with time, the personalized needs of users for indoor space layouts have become increasingly complex. Traditional indoor space layout design methods can no longer meet the needs of large market groups because of their complex steps and low levels of specialization. Therefore, this study first analyzes the problematic factors in indoor space layout design. Second, an interactive genetic algorithm is introduced to solve the multifactor optimal selection problem; the process is optimized and improved using a differential evolution algorithm. A comprehensive spatial layout model combining interactive genetic and differential evolution algorithms is proposed. The experimental results show that the model performs best with uniform variation, and its average number of iterations to find the optimal individual is 57. In addition, compared with similar layout models, the proposed model achieved the highest space utilization value of 79%, which is approximately 19% higher than that for the stacking layout model; it also required the shortest time, that is, 15 min. In summary, the proposed model provides a new intelligent method for indoor layout design, which is expected to improve the satisfaction of designers and users. [ABSTRACT FROM AUTHOR]

Chebyshev polynomials of the first kind are used to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on a segment is solved, and its approximate properties on Holder classes H¹ are analyzed. An exact equality is obtained for the deviation of Holder class functions from the generalized Chebyshev–Poisson integral. [ABSTRACT FROM AUTHOR]

The article considers the problem of reducing the losses caused by the implementation of threats to the topology of connections. Threats considered may relate to the integrity, confidentiality and availability of the information transmitted by the corresponding connection. At the same time, it is assumed that the amount of total funding allocated to protect against these threats is limited to a certain amount. This amount should be divided into parts, each of which will correspond to the financing of protection against a certain threat. A corresponding mathematical model was created to solve this problem. In this model, we make the reasonable assumption that the more funding is provided to protect against a threat, the less is the probability of its occuring. With this assumption, the problem is reduced to an optimization problem, which, generally speaking, cannot be solved by analytical methods. But for a small number of variables (up to 100 variables), this problem can be solved numerically using the tools of the Mathematica package. The article also provides the program code that implements the solution of this problem, and numerical examples of its solution using this code. [ABSTRACT FROM AUTHOR]

Applying a parametric approach, in this paper we studied a new class of multidimensional extremization models with data uncertainty. Concretely, first, we derived the robust conditions of necessary optimality. Thereafter, we established robust sufficient optimality conditions by employing the various forms of convexity of the considered functionals. In addition, we formulated an illustrative example to validate the theoretical results. [ABSTRACT FROM AUTHOR]

The sine cosine algorithm (SCA) and multi-verse optimizer (MVO) are the recognized optimization strategies frequently employed in numerous scientific areas. However, both SCA and MVO grapple with optimizing the transition between the exploitation and exploration mechanisms. Furthermore, MVO exhibits constraints in its exploitation capabilities. To tackle these limitations, this paper introduces a hybrid model termed SMVO, combining the advantages of both SCA and MVO. This hybrid approach seeks to harmonize exploitation and exploration stages by leveraging the unique advantages of each parent algorithm. The efficacy of SMVO was assessed using 23 benchmark test functions, revealing its competitive performance against not only SCA and MVO but also the ant lion optimization (ALO) and the dragonfly algorithm (DA). Additionally, SMVO's applicability was further validated by successfully addressing three distinct engineering optimization challenges, underscoring its stability and promise as a global optimization tool. [ABSTRACT FROM AUTHOR]

Optimizing the architecture of superconducting quantum processors is crucial for improving the efficiency of executing quantum programs. Existing schemes either modify general-purpose architectures, which might lead to an increase in the probability of qubit frequency collisions, or customize special-purpose architectures based on the quantum programs to reduce the gate operations after qubit mapping, but the architectures lack support for the post-mapping gate operations' optimization of multiple programs, which reduce their reusability. In this study, we propose a new processor architecture design method that reduces the average growth of the total post-mapping gate count on multiple quantum programs as well as to reduce the impact of processor architecture on frequency collisions, and thus improve the reusability of special-purpose processor. The main idea is to construct a new architecture by finding maximum common edge subgraph among multiple special-purpose processor architectures. To show the effectiveness of our method, we selected quantum programs with different functions covering 9 types of qubit numbers for comparison. Comprehensive simulation results show that the architecture schemes generated by using our method outperform two general-purpose architecture schemes based on the square lattice and the eff-5-freq's special-purpose architecture schemes, respectively. Compared to the all 2-qubit bus and the eff-5-freq's architecture schemes, after qubit mapping, the architecture schemes of our method have the smallest average growth of gate operations in multiple quantum programs (the largest average growth is 5.63%), which further supports the execution of different quantum programs. Meanwhile, the architecture schemes of our method also reduce the probability of frequency collisions by at least 4.48% compared to all other schemes. Furthermore, we compared our method with another special-purpose design method. In the schemes of different special-purpose architecture design methods, our method is able to generate architectures with better matching for multiple quantum programs. Therefore, our method can provide superconducting quantum processor architecture design with higher reusability for multiple quantum programs. [ABSTRACT FROM AUTHOR]

With the development of the Internet of Things (IoT) and cloud computing, various multimedia data such as audio, video, and images have experienced explosive growth, ushering in the era of big data. Large-scale computing tasks in the Multimedia Internet of Things (M-IoT), such as mathematical optimization problems, have begun to be outsourced from IoT devices with limited computing power to cloud servers for execution. However, outsourcing computation brings security concerns, because the behaviors of clouds are invisible to users. The leakage of privacy data in outsourced optimization problems leads to immeasurable losses. The mutual distrust between clouds and users causes that the correctness of the optimal decisions and the fairness of the payment activities are not guaranteed. Blockchain technology has the characteristic of immutability and has become a new security paradigm for eliminating multi-party trust concerns. In this article, we propose a Bitcoin-based secure outsourcing scheme to address the aforementioned security concerns. To prevent confidential data leakage, the proposed scheme designs a computable privacy-preserving method for the outsourced optimization problems. To judge the correctness of the optimal decision and reduce verification costs, the proposed scheme designs a low-cost two-layer verification mechanism based on dual theory and blockchain technology. Blockchain nodes reach a consensus on the problem solutions and trigger an automatic fair payment protocol-based Bitcoin. Security analysis and experimental results demonstrate that our scheme guarantees privacy, fairness, and computational efficiency. [ABSTRACT FROM AUTHOR]