Convergence Of Algorithm Research Articles

A Relaxed Version of the Cutting Method with Approximation of the Constraint Region

A cutting method was proposed for solving the convex programming problem. The method assumes that the constraint region of the problem is embedded into some polyhedral sets for constructing iteration points. It involves the construction of a sequence of approximations that belongs to the admissible set and is relaxed, as well as implies that the ε-solution of the initial problem is fixed after a finite number of steps. The method also allows to obtain mixed convergent algorithms by using, if desired, any known or new relaxation algorithms for constructing the main iteration points.

Strong convergent algorithm for finding minimum-norm solutions of quasimonotone variational inequalities with fixed point constraint and application

The class of quasimonotone mappings are known to be more general and applicable than the classes of pseudomonotone and monotone mappings. However, only very few results can be found in the literature on quasimonotone variational inequality problems and most of these results are on weak convergent algorithms. In this paper, we study the quasimonotone variational inequality problem (VIP) with constraint of fixed point problem (FPP) of quasi-pseudocontractive mappings. We introduce a new inertial Tseng’s extragradient method with self-adaptive step size for approximating the minimum-norm solutions of the aforementioned problem in the framework of Hilbert spaces. We prove that the sequence generated by the proposed method converges strongly to a common (minimum-norm) solution of the quasimonotone VIP and FPP of quasi-pseudocontractive mappings without the knowledge of the Lipschitz constant of the cost operator. We provide several numerical experiments for the proposed method in comparison with existing methods in the literature. Finally, we applied our result to image restoration problem. Our result improves, extends and generalizes several of the recently announced results in this direction.

Distributed Task Offloading and Resource Purchasing in NOMA-Enabled Mobile Edge Computing: Hierarchical Game Theoretical Approaches

As the computing resources and the battery capacity of mobile devices are usually limited, it is a feasible solution to offload the computation-intensive tasks generated by mobile devices to edge servers (ESs) in mobile edge computing (MEC) . In this article, we study the multi-user multi-server task offloading problem in MEC systems, where all users compete for the limited communication resources and computing resources. We formulate the offloading problem with the goal of minimizing the cost of the users and maximizing the profits of the ESs. We propose a hierarchical EETORP (Economic and Efficient Task Offloading and Resource Purchasing) framework that includes a two-stage joint optimization process. Then we prove that the problem is NP-complete. For the first stage, we formulate the offloading problem as a multi-channel access game (MCA-Game) and prove theoretically the existence of at least one Nash equilibrium strategy in MCA-Game. Next, we propose a game-based multi-channel access (GMCA) algorithm to obtain the Nash equilibrium strategy and analyze the performance guarantee of the obtained offloading strategy in the worst case. For the second stage, we model the computing resource allocation between the users and ESs by Stackelberg game theory, and reformulate the problem as a resource pricing and purchasing game (PAP-Game). We prove theoretically the property of incentive compatibility and the existence of Stackelberg equilibrium. A game-based pricing and purchasing (GPAP) algorithm is proposed. Finally, a series of both parameter analysis and comparison experiments are carried out, which validate the convergence and effectiveness of the GMCA algorithm and GPAP algorithm.

Hybrid optimization algorithm for estimating soil parameters of spoil hopper deposition model for trailing suction hopper dredgers

Trailing suction hopper dredger is a kind of hydraulic dredger, it has the characteristics of self-propelled, selfloading, self-dredging, self-unloading, it is the main force in dredging and blowing works, it is widely used in the world, it can be said that where there is a big dredging project where there is a trailing suction hopper dredger’s figure. The loading optimization process of trailing suction hopper dredger contains a lot of dredging parameters related to soil type, and the soil type under different working conditions is not very clear. In this study, we present a hybrid optimization technique based on simulated annealing and multi-population genetic algorithm to enhance the loading efficiency of a trailing suction hopper dredger and to examine the variation of dredged soil parameters. The soil parameters of the spoil hopper deposition model were estimated using this hybrid optimization algorithm. The experimental results show that the soil parameters are successfully estimated and verified by our measured construction data of a trailing suction hopper dredger. In addition, our proposed method has the highest accuracy of soil parameter estimation, the fastest algorithm convergence, and excellent robustness compared to the other three intelligent optimization methods. In addition, our method successfully avoids the phenomenon of premature convergence that usually occurs in traditional genetic algorithms, and the parameters show strong adaptability to different vessels under the same dredging area.

Convergence of the Harris hawks optimization algorithm and fuzzy system for cloud-based task scheduling enhancement

Convergence of the Harris hawks optimization algorithm and fuzzy system for cloud-based task scheduling enhancement

A whale optimization algorithm based on atom-like structure differential evolution for solving engineering design problems

The whale optimization algorithm has received much attention since its introduction due to its outstanding performance. However, like other algorithms, the whale optimization algorithm still suffers from some classical problems. To address the issues of slow convergence, low optimization precision, and susceptibility to local convergence in the whale optimization algorithm (WOA). Defining the optimization behavior of whale individuals as quantum mechanical behavior, a whale optimization algorithm based on atom-like structure differential evolution (WOAAD) is proposed. Enhancing the spiral update mechanism by introducing a sine strategy guided by the electron orbital center. Improving the random-walk foraging mechanism by applying mutation operations to both the electron orbital center and random individuals. Performing crossover operations between the newly generated individuals from the improved mechanisms and random dimensions, followed by a selection process to retain superior individuals. This accelerates algorithm convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Finally, implementing a scouting bee strategy, where whale individuals progressively increase the number of optimization failures within a limited parameter L. When a threshold is reached, random initialization is carried out to enhance population diversity. Conducting simulation experiments to compare the improved algorithm with the whale optimization algorithm, other optimization algorithms, and other enhanced whale optimization algorithms. The experimental results indicate that the improved algorithm significantly accelerates convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Applying the improved algorithm to five engineering design problems, the experimental results demonstrate that the improved algorithm exhibits good applicability.

A first-order computational algorithm for reaction-diffusion type equations via primal-dual hybrid gradient method

We propose an easy-to-implement iterative method for resolving the implicit (or semi-implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the nonlinear time implicit scheme as a min-max saddle point problem and then apply the primal-dual hybrid gradient (PDHG) method. Suitable precondition matrices are applied to the PDHG method to accelerate the convergence of algorithms under different circumstances. Furthermore, our method is applicable to various discrete numerical schemes with high flexibility. From various numerical examples tested in this paper, the proposed method converges properly and can efficiently produce numerical solutions with sufficient accuracy.

A Selection of Starting Points for Iterative Position Estimation Algorithms Using Feedforward Neural Networks.

This article proposes the use of a feedforward neural network (FNN) to select the starting point for the first iteration in well-known iterative location estimation algorithms, with the research objective of finding the minimum size of a neural network that allows iterative position estimation algorithms to converge in an example positioning network. The selected algorithms for iterative position estimation, the structure of the neural network and how the FNN is used in 2D and 3D position estimation process are presented. The most important results of the work are the parameters of various FNN network structures that resulted in a 100% probability of convergence of iterative position estimation algorithms in the exemplary TDoA positioning network, as well as the average and maximum number of iterations, which can give a general idea about the effectiveness of using neural networks to support the position estimation process. In all simulated scenarios, simple networks with a single hidden layer containing a dozen non-linear neurons turned out to be sufficient to solve the convergence problem.

Decision variable classification based multi-objective multifactorial memetic algorithm for multi-objective multi-task optimization problem

Multi-task multi-objective optimization problems need to consider the algorithm's convergence and the population's diversity. The information transfer of decision variables with different characteristics may harm the effect of knowledge reuse. This paper proposes a novel hybrid multi-objective multifactorial memetic algorithm to address this issue. The proposed variable classification method will classify decision variables into convergence-related and diversity-related decision variables. Only the same type of decision variables in the source and target tasks can transfer information to avoid negative transfer. Different evolutionary operators are adopted according to the characteristics of decision variables during individual recombination. In addition, the proposed algorithm hybridizes the immune algorithm as the global evolutionary operator and the evolutionary gradient search algorithm as the local search operator into the multifactorial framework to enhance the searching ability. Finally, the proposed algorithm is compared with the state-of-the-art multi-objective evolutionary multitasking algorithms. The results of the experiments show that the proposed algorithm can achieve promising performance on the classical and complex multi-task multi-objective benchmark test suites.

Proximal Policy Optimization for Efficient D2D-Assisted Computation Offloading and Resource Allocation in Multi-Access Edge Computing

In the advanced 5G and beyond networks, multi-access edge computing (MEC) is increasingly recognized as a promising technology, offering the dual advantages of reducing energy utilization in cloud data centers while catering to the demands for reliability and real-time responsiveness in end devices. However, the inherent complexity and variability of MEC networks pose significant challenges in computational offloading decisions. To tackle this problem, we propose a proximal policy optimization (PPO)-based Device-to-Device (D2D)-assisted computation offloading and resource allocation scheme. We construct a realistic MEC network environment and develop a Markov decision process (MDP) model that minimizes time loss and energy consumption. The integration of a D2D communication-based offloading framework allows for collaborative task offloading between end devices and MEC servers, enhancing both resource utilization and computational efficiency. The MDP model is solved using the PPO algorithm in deep reinforcement learning to derive an optimal policy for offloading and resource allocation. Extensive comparative analysis with three benchmarked approaches has confirmed our scheme’s superior performance in latency, energy consumption, and algorithmic convergence, demonstrating its potential to improve MEC network operations in the context of emerging 5G and beyond technologies.

Differential Mutation Incorporated Quantum Honey Badger Algorithm with Dynamic Opposite Learning and Laplace Crossover for Fuzzy Front-End Product Design.

In this paper, a multi-strategy fusion enhanced Honey Badger algorithm (EHBA) is proposed to address the problem of easy convergence to local optima and difficulty in achieving fast convergence in the Honey Badger algorithm (HBA). The adoption of a dynamic opposite learning strategy broadens the search area of the population, enhances global search ability, and improves population diversity. In the honey harvesting stage of the honey badger (development), differential mutation strategies are combined, selectively introducing local quantum search strategies that enhance local search capabilities and improve population optimization accuracy, or introducing dynamic Laplacian crossover operators that can improve convergence speed, while reducing the odds of the HBA sinking into local optima. Through comparative experiments with other algorithms on the CEC2017, CEC2020, and CEC2022 test sets, and three engineering examples, EHBA has been verified to have good solving performance. From the comparative analysis of convergence graphs, box plots, and algorithm performance tests, it can be seen that compared with the other eight algorithms, EHBA has better results, significantly improving its optimization ability and convergence speed, and has good application prospects in the field of optimization problems.

Linear convergence of a primal-dual algorithm for distributed interval optimization

<abstract><p>In this paper, we investigate a distributed interval optimization problem whose local functions are interval functions rather than scalar functions. Focusing on distributed interval optimization, this paper presents a distributed primal-dual algorithm. A criterion is introduced under which linear convergence to the Pareto solution of distributed interval optimization problems can be achieved without strong convexity. Lastly, a numerical simulation is presented to illustrate the linear convergence of the algorithm that has been proposed.</p></abstract>

ОБҐРУНТУВАННЯ ПАРАМЕТРІВ МЕТОДУ РОЗРАХУНКУ ХАРАКТЕРИСТИК ЕЛЕКТРОМАГНІТНОГО РОЗСІЮВАННЯ МЕТАЛЕВОЇ НАНОЧАСТИНКИ У ОПТИЧНОМУ ДІАПАЗОНІ

Structures of nanoparticles of noble metals in the optical range are of great interest in solving practical problems of building and using optical antennas and sensors for communication, creating solar cells, coatings for masking objects in the optical range and their detection. Currently, intensive research is being carried out on resonance effects during the scattering and absorption of light by such nanosized particles. There are both experimental methods of studying the characteristics of electromagnetic scattering of nanostructures in the optical range, and methods of mathematical modeling. Mathematical methods are subject to strict requirements regarding accuracy and ensuring the convergence of calculation results. The method of integral equations is widely used to model scattering from various objects with finite dielectric constants. At the same time, in the optical range, scattering on nanoparticles, as homogeneous resonant objects, has its own characteristics that affect the accuracy and convergence of the calculation algorithm. The article examines the issue of choosing and justifying the parameters of the method for calculating the characteristics of electromagnetic scattering of nanoparticles of noble metals of different sizes in the optical range, which are based on the application of a system of Müller integral equations. The internal convergence of the algorithm for calculating electromagnetic scattering characteristics depends on the size and shape of nanoparticles. When calculating according to the proposed numerical method, the number of nodes in which the current density was calculated was chosen in such a way that there was an internal convergence of the algorithm characterized by a given value . The required number of current nodes and the discretization step on the surface of one nanoparticle of two sizes (75x75x25 and 100x100x20) were obtained, which ensure internal convergence and the best accuracy of the proposed computational algorithm. Nanoparticles of these sizes will be used as the basis for the construction of various structures. The direction of further research is obtaining and analyzing the characteristics of electromagnetic scattering of various structures made of silver nanoparticles under different conditions of irradiation and polarization of the incident electromagnetic wave.

Inverse Value Iteration and Q -Learning: Algorithms, Stability, and Robustness.

This article proposes a data-driven model-free inverse Q -learning algorithm for continuous-time linear quadratic regulators (LQRs). Using an agent's trajectories of states and optimal control inputs, the algorithm reconstructs its cost function that captures the same trajectories. This article first poses a model-based inverse value iteration scheme using the agent's system dynamics. Then, an online model-free inverse Q -learning algorithm is developed to recover the agent's cost function only using the demonstrated trajectories. It is more efficient than the existing inverse reinforcement learning (RL) algorithms as it avoids the repetitive RL in inner loops. The proposed algorithms do not need initial stabilizing control policies and solve for unbiased solutions. The proposed algorithm's asymptotic stability, convergence, and robustness are guaranteed. Theoretical analysis and simulation examples show the effectiveness and advantages of the proposed algorithms.

A Nonlocal Self-Similarity-Based Weighted Tensor Low-Rank Decomposition for Multichannel Image Completion With Mixture Noise.

Multichannel image completion with mixture noise is a challenging problem in the fields of machine learning, computer vision, image processing, and data mining. Traditional image completion models are not appropriate to deal with this problem directly since their reconstruction priors may mismatch corruption priors. To address this issue, we propose a novel nonlocal self-similarity-based weighted tensor low-rank decomposition (NSWTLD) model that can achieve global optimization and local enhancement. In the proposed model, based on the corruption priors and the reconstruction priors, a pixel weighting strategy is given to characterize the joint effects of missing data, the Gaussian noise, and the impulse noise. To discover and utilize the accurate nonlocal self-similarity information to enhance the restoration quality of the details, the traditional nonlocal learning framework is optimized by employing improved index determination of patch group and handling strip noise caused by patch overlapping. In addition, an efficient and convergent algorithm is presented to solve the NSWTLD model. Comprehensive experiments are conducted on four types of multichannel images under various corruption scenarios. The results demonstrate the efficiency and effectiveness of the proposed model.

On the design of cost minimization for D2D‐enabled wireless caching networks: A joint recommendation, caching, and routing perspective

AbstractCache‐enabled device‐to‐device (D2D) network has been deemed as an effective technique to offload the data traffic. However, the gain of the caching schemes is closely related to the homogeneity among users' preference distribution. To tackle this issue, recommendation is a promising proactive approach. It increases the request probability of recommended contents, reshaping users' contents demand patterns, and improving caching performance. Moreover, considering the heterogeneous network settings, i.e. content retrieval costs vary, the routing design becomes a non‐negligible factor on caching performance optimization. On these grounds, the average system cost of D2D‐enabled wireless caching networks with multiple BSs is first described. Then the routing strategies are designed together with caching and recommendation policies by minimizing the average cost of these networks. The optimization problem is proven as NP‐hard. To facilitate the analysis, the original problem is decoupled into two sub‐problems and solve them respectively. Afterwards, all the variables are optimized in an alternating manner until the convergence is achieved. The proposed algorithm's convergence performance and benefits over benchmark strategies in terms of total cost and cache hit ratio are supported by Monte‐Carlo simulation results.

A recent proximal gradient algorithm for convex minimization problem using double inertial extrapolations

<abstract><p>In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance the algorithm's convergence rate. We establish a weak convergence theorem under some mild conditions. Furthermore, we perform numerical tests, and apply the algorithm to image restoration and data classification as a practical application. The experimental results show our approach's superior performance and effectiveness, surpassing some existing methods in the literature.</p></abstract>

Protocol using similarity score and improved shrink-wrap algorithm for better convergence of phase-retrieval calculation in X-ray diffraction imaging.

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi etal.(2017), J. Synchrotron Rad. 24, 1024-1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

A New Inertial-Projection Method for Solving Split Generalized Mixed Equilibrium and Hierarchical Fixed Point Problems

In this paper, we introduce a new iterative algorithm of inertial form for approximating the common solution of Split Generalized Mixed Equilibrium Problem (SGMEP) and Hierarchical Fixed Point Problem (HFPP) in real Hilbert spaces. Motivated by the subgradient extragradient method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity and lower semicontinuity of the SGMEP and HFPP associated mappings, we establish the strong convergence of the iterative algorithm. Some numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature.

A Bi‐Objective Stochastic Model of Locating‐Allocating‐Routing Relief and Rescue in Disaster Response Conditions: An Accelerated Benders Decomposition

Problem Statement. Proper and timely relief in the postdisaster phase is very important to minimize victims and casualties. It is necessary to assess the needs of the affected points and provide relief in the shortest possible time without wasting time. For this purpose, it is necessary and vital to determine the location of care centers, temporary accommodation centers, and routing to distribution vital and medical items. The Proposed Approach. In this paper, using a scenario‐based stochastic planning mathematical model, postdisaster relief is discussed. Also, attention has been paid to the distribution of vital items by using routing. Contributions. By using the epsilon constraint method, a strong efficient solution has been achieved for model’s objectives, and also a sensitivity analysis has been performed on some of the model’s parameters. Also, an accelerated stochastic benders decomposition algorithm is suggested to solve the problem modeled in this paper. To speed up the convergence of the solution algorithm, valid inequalities are introduced to get better quality lower bounds. Results. The results of the research show that the simultaneous consideration of the relief evacuation and distribution process improves the relief logistics process.