Bangmod International Journal of Mathematical and Computational Science

The Hybrid Steepest Descent Method with Implicit Double Midpoint for Solving Variational Inequality over Triple Hierarchical Problems

2025-01-10T16:42:35+00:00

Because of the importance of the variational inequality problem that related to many other problems in various branches of science and engineering, it becomes one of the most popular topics which many researchers pay deeply attention to study on the way to solve and the way to apply. In this research, we study the monotone variational inequality over triple hierarchical problem. We propose a new implicit algorithm to find the solution with the strong convergence theorem which is proved and applied to guarantee its solution under some weak assumptions. Our results enhance those of Xu et al., Ke and Ma, Dhakal and Wutiphol and many other authors.

A Two-Step Inertial CQ Method for Split Feasibility Problems with Applications

2025-03-07T10:29:34+00:00

This paper introduces an algorithm for approximating solutions of split feasibility problems by employing a two-step inertial acceleration strategy along with a self-adaptive step size. This combination enhances the convergence rate and reduces computational complexity of the proposed algorithm. The nonasymptotic O(1/t) convergence rate and global convergence of the proposed method are established within the context of Euclidean spaces. The algorithm is extended to handle multiple set split feasibility problems, and a sensitivity analysis is conducted to identify optimal inertial parameter choices. Additionally, the algorithm is applied to the LASSO problem. Comparative evaluations with various algorithms from existing literature showcase the superior performance of the proposed algorithm.

The Plethystic Exponentials Created in Certain Domains of the Complex Plane and Related Implications

2025-01-09T09:58:42+00:00

The primary aim of this scientific investigation is to introduce basic information about plethystic exponential forms, which play significant roles in both mathematics and related fields. It then aims to reorganize these concepts within specific regions of the complex plane, focus on new complex ideas, and present various propositions, along with their implications and potential applications, for consideration by relevant researchers.

Guaranteed Pursuit Time for an Inﬁnite System in \(l_2\) with Geometric Constraints

2024-06-21T19:39:36+00:00

In this paper, we consider a pursuit differential game problem described by an infinite system of binary differential equations in the Hilbert space \(l_2\). The control parameters of the players are subject to geometric constraints. The pursuer's goal is to complete the game by bringing the state of the system to the origin, while the evader's goal is the contrary. The guaranteed pursuit time required to achieve the pursuer's goal is estimated. To this end, we constructed
an optimal strategy for the pursuer.

Controlling the Spread of Malaria-Cholera Co-infection with Effective Intervention Strategy

2024-12-26T19:53:31+00:00

This paper proposes an optimal control of intervention strategies for malaria-cholera co-infection with emphasis on five control strategies namely: treated bed nets, treatments of malaria, indoor residual spray, sanitation and treatment of cholera to prevent disease spread in a population. A non-linear system of differential equations is formulated to study the dynamics of the proposed model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) states were obtained. The basic reproduction numbers, \(\mathcal{R}_0^{C},\,\mathcal{R}_0^{V}\) that determine the transmission of the diseases were derived. A sensitivity analysis on the reproduction numbers to determine the parameters that have impact on the reproduction number were carried out. Using the Routh-Hurwitz criterion and Castillo-Chavez techniques, the conditions for stability of the disease-free equilibrium were established. The result of the stability revealed that, if the reproduction number is kept below to unity, malaria-cholera co-infection can be entirely eradicated. The sensitivity analysis results paved way for the implementation of a controlled system, which was solved using Pontryagin's Maximum Principle (PMP) and an optimality system was obtained. The optimality system was then solved numerically using forward backward sweep approach and graphs were produced.

Strong Convergence Accelerated Alternated Inertial Relaxed Algorithm for Split Feasibilities with Applications in Breast Cancer Detection

2024-10-06T03:12:01+00:00

In this article, we construct an accelerated relaxed algorithm with an alternating inertial extrapolation step. The proposed algorithm uses a three-term conjugate gradient-like direction, which helps to fasten the sequence of its iterates to a point in a solution set. The algorithm employs a self-adaptive step-length criterion that does not require any information related to the norm of the operator or the use of a line-search procedure. Moreover, we formulate and prove a strong convergence theorem for the algorithm to a minimum-norm solution of a split feasibility problem in infinite-dimensional real Hilbert spaces. Furthermore, we investigate its applications in breast cancer detection by solving classification problems for an interesting real-world breast cancer dataset, based on the extreme learning machine (ELM) with the \(\ell_{1}\)-regularization approach (i.e., the Lasso model) and the \(\ell_{1}\)-\(\ell_{2}\) hybrid regularization technique. The performance results of the experiments demonstrate that the proposed algorithm is robust, efficient, and achieves better generalization performance and stability than some existing algorithms in the literature.