Variational Inclusion Problems Research Articles

A modified projective forward-backward splitting algorithm for variational inclusion problems to predict Parkinson's disease

This research studies variational inclusion problems, which is a branch of optimization. A modified projective forward-backward splitting algorithm is constructed to solve this problem. The algorithm adds the inertial technique for speeding up the convergence, and the projective method for several regularization machine learning models to meet good model fitting. To evaluate the performance of the classification models employed in this research, four evaluation metrics are computed: accuracy, F1-score, recall, and precision. The highest performance value of 92.86% accuracy, 62.50% precision, 100% recall, and 76.92% F1-score shows that our algorithm performs better than the other machine learning models.

Modified proximal point algorithms for variational inclusion problems on Hadamard manifolds

Modified proximal point algorithms for variational inclusion problems on Hadamard manifolds

The AA-Viscosity Algorithm for Fixed-Point, Generalized Equilibrium and Variational Inclusion Problems

The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.

Viscosity-type inertial iterative methods for variational inclusion and fixed point problems

<abstract><p>In this paper, we have introduced some viscosity-type inertial iterative methods for solving fixed point and variational inclusion problems in Hilbert spaces. Our methods calculated the viscosity approximation, fixed point iteration, and inertial extrapolation jointly in the starting of every iteration. Assuming some suitable assumptions, we demonstrated the strong convergence theorems without computing the resolvent of the associated monotone operators. We used some numerical examples to illustrate the efficiency of our iterative approaches and compared them with the related work.</p></abstract>

Tseng-type algorithms for solving variational inequalities over the solution sets of split variational inclusion problems with an application to a bilevel optimization problem

Tseng-type algorithms for solving variational inequalities over the solution sets of split variational inclusion problems with an application to a bilevel optimization problem

Relaxed double inertial Tseng's extragradient method for solving non-Lipschitz split monotone variational inclusion problems with fixed point constraints

Relaxed double inertial Tseng's extragradient method for solving non-Lipschitz split monotone variational inclusion problems with fixed point constraints

Iterative Algorithm of Split Monotone Variational Inclusion Problem for New Mappings

In this paper, we developed a new type iterative scheme to approximate a common solution of split monotone variational inclusion, variational inequality and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we proved that the sequence generated by the proposed iterative method converges strongly to a common solution of split monotone variational inclusion, variational inequality and fixed point problems. Furthermore, we give some consequences of the main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm. The result presented in this paper unifies and extends some known results in this area.

A projective double inertial forward-backward splitting algorithm for variational inclusion problems application to data classification

A projective double inertial forward-backward splitting algorithm for variational inclusion problems application to data classification

Strong convergence for split variational inclusion problems under hybrid algorithms with applications

In this article, we present two inertial modifications of regularized algorithms for the split variational inclusion problem (SVIP, for short) in real Hilbert spaces (RHSs). When the circumstances are right, strong convergence theorems are demonstrated. The major findings are used to solve the split minimization, split common fixed point problem (SCFPP), split minimization problem (SMP), and split feasibility problems (SFP) in applications. The proposed algorithms are contrasted with a number of other existing algorithms in the literature in order to test their numerical performances. Finally, the computer tests demonstrate that the suggested algorithms outperform alternative strategies in terms of speed and efficiency.

CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM

This article aims to define a new resolvent operator for variational inclusion problems in the framework of Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim. Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study.

Dynamic stepsize iteration process for solving split common fixed point problems with applications

In this paper, we study the split common fixed point problem for two nonlinear mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm.

A new projection algorithm for variational inclusion problems and its application to cervical cancer disease prediction

This study proposes a new projection algorithm for solving variational inclusion problems that exhibit weak convergence under suitable conditions in Hilbert space. Furthermore, we apply our algorithm to solve data classification using the cervical cancer behavior risk dataset. The comparison is done in terms of accuracy, precision, recall, and F1-score with other literature. Our proposed algorithm has proved to be more performant than other benchmark techniques for solving regularized least squares problems with different norms.

A Regularized Tseng Method for Solving Various Variational Inclusion Problems and Its Application to a Statistical Learning Model

We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.

An algorithm for approximating solutions of the split variational inclusion problem

We introduce and study an iterative algorithm to approximate a solution to the split variational inclusion problem in real Hilbert spaces. The strong convergence of the proposed algorithm is proved via some suitable conditions. As applications, we derive consequences for several special cases such as the split variational inequality problem, the split minimum point problem, and the split common fixed point problem. Finally, we present some numerical experiments to demonstrate the performance of the proposed algorithm.

Convergence analysis of the generalized viscosity explicit method for solving variational inclusion problems in Banach spaces with applications

In this paper, we develop the viscosity explicit method for finding a solution of the variational inclusion problem, which is a zero of the sum of two accretive operators, in Banach spaces which integrates the algorithm defined by Cholamjiak, Pholasa, Suantai, and Sunthrayuth [The generalized viscosity explicit rules for solving variational inclusion problems in Banach spaces. Optimization. 2021;70(12):2607–2633. doi: 10.1080/02331934.2020.1789131] and the algorithm defined by Wang, Wang, and Zhang [Strong convergence of viscosity forward-backward algorithm to the sum of two accretive operators in Banach space. Optimization. 2021;70(1):169–190. doi: 10.1080/02331934.2019.1705299]. Also, we provide a new suitable assumption to prove the strong convergence theorem. We apply our main result to the variational inequality problem, the convex minimization problem, and the split feasibility problem. Numerical examples are given to illustrate the performance of the proposed method in the comparison with the related methods.

An approximation algorithm for solving a split problem of fixed point and variational inclusion

In this paper, the split fixed point and variational inclusion problems are considered. With the help of fixed point technique, Tseng-type splitting method and self-adaptive rule, an iterative algorithm is proposed for solving this split problem in which the involved operators f and g are demicontractive operators and ϕ is plain monotone. Strong convergence theorem is proved under some mild conditions.

New inertial modification of regularized algorithms for solving split variational inclusion problem

In this paper, we introduce two new self-adaptive iterative algorithms for finding the solution of a split variational inclusion problem in real Hilbert spaces. The strong convergence theorems are proved under suitable conditions. In applications, the main results are applied for solving the split feasibility problem, the split minimization problem, and the split common fixed point problem. In order to test the numerical performances, the proposed algorithms are compared with several existing algorithms in the literature. Finally, the computational experiments show that the proposed algorithms are fast and more efficient than other approaches.

Perturbation Resilience of Self-Adaptive Step-Size Algorithms for Solving Split Variational Inclusion Problems and their Applications

In this paper, two viscosity proximal type algorithms involving the superiorization method are presented for solving the split variational inclusion problems in real Hilbert spaces. Strong convergence theorems and bounded perturbation resilience analysis of the proposed algorithms are obtained under mild conditions. The split feasibility problems, the split minimization problems, and the variational inequality problems are concerned as the applications, and several numerical experiments are performed to show the efficiency and implementation of the proposed algorithms.

A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces

A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces

Viscosity approximation method for split best proximity point and monotone variational inclusion problem

ABSTRACT To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper.