Multiple-output Setting Research Articles

Relaxed inertial self-adaptive algorithm for the split feasibility problem with multiple output sets and fixed-point problem in the class of demicontractive mappings

The purpose of this paper is to study the split feasibility problem with multiple output sets and fixed point problem in the class of demicontractive mappings and propose relaxed inertial self-adaptive algorithms that do not use the least squares method. Under some appropriate assumptions, we establish a strong convergence result for the sequence generated by the proposed algorithm. Our result generalizes and extends several results existing in the literature. Finally, we illustrate the convergence of the proposed algorithm by using a numerical example.

A Relaxed Tseng’s Method-based Algorithm for Solving Split Variational Inequalities with Multiple Output Sets

In this paper, the split variational inequality problem with multiple output sets is considered in a more general framework of reflexive Banach spaces. We introduce a relaxed Tseng extragradient method for approximating the solution of this problem when the cost operators are pseudomonotone and non-Lipschitz. Moreover, our proposed algorithm employs the inertial technique and a new self-adaptive step size to guarantee high rate of convergence. Strong convergence of the algorithm is proved in this case without the need for the sequential weak continuity condition. Finally, some numerical experiments are given to show the applicability of our proposed algorithm.

RELAXED DOUBLE INERTIA AND VISCOSITY ALGORITHMS FOR THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

In this paper, we investigate a multiple-sets split feasibility problem with multiple output sets in infinite-dimensional Hilbert spaces. To address this problem, we propose relaxed inertial self-adaptive algorithms that do not use the least squares method and prove strong convergence results for the sequences generated by these algorithms. Finally, we validate the performances of the proposed algorithms by using numerical examples.

Convergence Result for Solving the Split Fixed Point Problem with Multiple Output Sets in Nonlinear Spaces

Convergence Result for Solving the Split Fixed Point Problem with Multiple Output Sets in Nonlinear Spaces

Two novel two-step inertial algorithms for a class of bilevel variational inequalities

This paper introduces two novel two-step inertial and self-adaptive step sizes algorithms for solving a strongly monotone variational inequality over the solution set of a split convex feasibility problem with multiple output sets in real Hilbert spaces. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve monotone variational inequalities over the solution set of the split feasibility problem. The method is further applied to the image classification problem via the support vector machine learning. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature.

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

Correction: Convergence theorem for fixed point and split generalized variational inclusion problems with multiple output sets in Banach spaces

Correction: Convergence theorem for fixed point and split generalized variational inclusion problems with multiple output sets in Banach spaces

Traffic network analysis via multidimensional split variational inequality problem with multiple output sets

<abstract><p>In this study, we introduce and investigate a new class of split inverse problems, comprising a multidimensional parameter of evolution, which we call the multidimensional split variational inequality problem with multiple output sets. To demonstrate its applicability, we formulate the equilibrium flow of multidimensional traffic network models for an arbitrary number of locations. We define a multidimensional split Wardrop condition with multiple output sets and establish its equivalence with the formulated equilibrium flow of multidimensional traffic network models. We then establish the existence and uniqueness of equilibria for our proposed model. In addition, we propose a method for solving the introduced problem. We then validate our results using some numerical experiments.</p></abstract>

Two self-adaptive CQ algorithms for the split feasibility problem with multiple output sets

Two self-adaptive CQ algorithms for the split feasibility problem with multiple output sets

Mann-Type Inertial Projection and Contraction Method for Solving Split Pseudomonotone Variational Inequality Problem with Multiple Output Sets

In this paper, we study the concept of split variational inequality problem with multiple output sets when the cost operators are pseudomonotone and non-Lipschitz. We introduce a new Mann-type inertial projection and contraction method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces. Under some mild conditions on the control parameters and without prior knowledge of the operator norms, we prove a strong convergence theorem for the proposed algorithm. We point out that while the cost operators are non-Lipschitz, our proposed method does not require any linesearch method but uses a more efficient self-adaptive step size technique that generates a non-monotonic sequence of step sizes. Finally, we apply our result to study certain classes of optimization problems and we present several numerical experiments to illustrate the applicability of the proposed method. Several of the existing results in the literature could be viewed as special cases of our result in this study.

New iterative algorithms for solving a class of split common solution problems and their applications

The purpose of this paper is to introduce new iterative algorithms for approximating a solution to a class of monotone operator equations. More precisely, we study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces. In order to solve this problem, we propose three new algorithms and establish strong convergence theorems for them.

ON SPLIT GENERALIZED EQUILIBRIUM AND FIXED POINT PROBLEMS OF BREGMAN W-MAPPINGS WITH MULTIPLE OUTPUT SETS IN REFLEXIVE BANACH SPACES

In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.

A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces

A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem with multiple output sets, subject to some reasonable control sequence restrictions. The suggested algorithm and its immediate consequences are also discussed. The effectiveness of the proposed algorithm is finally demonstrated through analytical examples. The findings presented in this paper will help to consolidate, extend, and improve upon a number of recent findings in the literature.

An inertial-type algorithm for a class of bilevel variational inequalities with the split variational inequality problem constraints

In this paper, we investigate the problem of solving strongly monotone variational inequalities over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces and establish a new iterative algorithm for it. Our algorithms are accelerated by the inertial technique and eliminate the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operator by employing a self-adaptive step size criterion. The strong convergence result is given under some mild conditions widely used in the convergence analysis. Two corollaries for the solutions of the split variational inequality problem and the split feasibility problem with multiple output sets are also obtained using our main result. Finally, some numerical experiments have been conducted to illustrate the effectiveness of the proposed algorithms and compare them with the related ones.

An algorithm for a class of variational inequalities with the split common fixed point problem with multiple output sets constraints

In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generated by the algorithm method is established without the prior knowledge of the norms of the given bounded linear operators. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, we include several numerical examples that serve to illustrate the performance of our proposed algorithm.

On split generalized equilibrium problem with multiple output sets and common fixed points problem

Abstract In this article, we introduce and study the notion of split generalized equilibrium problem with multiple output sets (SGEPMOS). We propose a new iterative method that employs viscosity approximation technique for approximating the common solution of the SGEPMOS and common fixed point problem for an infinite family of multivalued demicontractive mappings in real Hilbert spaces. Under mild conditions, we prove a strong convergence theorem for the proposed method. Our method uses self-adaptive step size that does not require prior knowledge of the operator norm. The results presented in this article unify, complement, and extend several existing recent results in the literature.

Mann-type approximation scheme for solving a new class of split inverse problems in Hilbert spaces

ABSTRACT In this paper, we introduce and study a new class of split inverse problems, named split hierarchical monotone variational inclusion problem with multiple output sets in real Hilbert spaces. By using the inertial technique and self-adaptive step size strategy, we propose and analyze a new Mann-type iterative method for solving the problem. The convergence analysis of the proposed iterative method under some suitable conditions is studied. Also, we show that the sequence of iterates generated by this method converges strongly to a minimum-norm solution of the problem. As theoretical applications, we apply our results to approximate the solutions of other classes of split inverse problems. Finally, we present some numerical experiments to illustrate the practical potential and advantages of our proposed method.

Variational inequalities over the solution sets of split variational inclusion problems

We study variational inequalities over the solution sets of split variational inclusion problems with multiple output sets. In order to find a solution to such problems, we introduce a new parallel iterative algorithm by combining the inertial forward–backward splitting method with the steepest descent method. Our algorithm does not depend on the norm of the transfer mappings. Some of its applications to solving split common null point, split minimum point, and split common fixed point problems are also given.

New Algorithms for Solving the Split Common Zero Point Problem in Hilbert Space

We introduce new self-adaptive algorithms for solving the split common zero point problem with multiple output sets in Hilbert space. We also apply our main results to solving split feasibility problems with multiple output sets.

Two new self-adaptive algorithms for solving split common fixed point problems with multiple output sets

In this paper, we study split common fixed point problems with multiple output sets in Hilbert spaces. For solving this problem, we improve Reich and Tuyen's algorithms [10] and propose two new self-adaptive algorithms which do not need any priori information on the norms of the transfer operators. Then, we establish weak convergence theorems for them. It can be seen from our numerical experiments that the proposed methods depict a very significant improvement in terms of the number of iterations and execution time.