Showing papers by "Lateef Olakunle Jolaoso published in 2021"

Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems

Abstract: In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the setting of Hilbert space. We...

Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space

Abstract: In this paper, we propose a new viscosity type inertial extragradient method with Armijo line-search technique for approximating a common solution of equilibrium problem with pseudo-monotone bifunc...

Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

Abstract: We propose a parallel iterative scheme with viscosity approximation method which converges strongly to a solution of the multiple-set split equality common fixed point problem for quasi-pseudocontractive mappings in real Hilbert spaces. We also give an application of our result to approximation of minimization problem from intensity-modulated radiation therapy. Finally, we present numerical examples to demonstrate the behaviour of our algorithm. This result improves and generalizes many existing results in literature in this direction.

Inertial-Type Algorithm for Solving Split Common Fixed Point Problems in Banach Spaces

Abstract: In this paper, motivated by the works of Kohsaka and Takahashi (SIAM J Optim 19:824–835, 2008) and Aoyama et al. (J Nonlinear Convex Anal 10:131–147, 2009) on the class of mappings of firmly nonexpansive type, we explore some properties of firmly nonexpansive-like mappings [or mappings of type (P)] in p-uniformly convex and uniformly smooth Banach spaces. We then study the split common fixed point problems for mappings of type (P) and Bregman weak relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an inertial-type shrinking projection algorithm for solving the two-set split common fixed point problems and prove a strong convergence theorem. Also, we apply our result to the split monotone inclusion problems and illustrate the behaviour of our algorithm with several numerical examples s. The implementation of the algorithm does not require a prior knowledge of the operator norm. Our results complement many recent results in the literature in this direction. To the best of our knowledge, it seems to be the first to use the inertial technique to solve the split common fixed point problems outside Hilbert spaces.

A new approximation scheme for solving various split inverse problems

Abstract: In this paper, we study the split equality problem for systems of monotone variational inclusions and fixed point problems of set-valued demi-contractive mappings in real Hilbert spaces. A new viscosity algorithm for solving this problem is introduced along with its strong convergence theorem. Several known theoretical applications, such as, split common null point problem for systems of monotone variational inclusions and fixed point problems, split equality saddle-point and fixed point problem are given. Two primary numerical examples which illustrate and compare the behavior of the new scheme, suggest that the method has a potential applicable value besides its theoretical generalization. Our work extends and generalizes some existing works in the literature as well as provide some new direction for future work.

Inertial algorithm with self-adaptive step size for split common null point and common fixed point problems for multivalued mappings in Banach spaces

Abstract: In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone opera...

Single Bregman projection method for solving variational inequalities in reflexive Banach spaces

Abstract: In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is des...

A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

Abstract: In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

Strong convergence theorems for finite families of pseudomonotone equilibrium and fixed point problems in Banach spaces

Abstract: In this article, we introduce a new linesearch technique with Halpern iteration for finding a common solution of finite families of pseudomonotone equilibrium problems and fixed point of finite family of quasi- $$\phi $$ -nonexpansive mappings in Banach spaces. Under standard assumptions imposed on the equilibrium bifunctions and the quasi- $$\phi $$ -nonexpansive mappings, we proved that the sequence generated by our algorithm converges strongly to the unique solution of the equilibrium and fixed point problems. Numerical example is presented to illustrate the efficiency and accuracy of the proposed algorithm. Our results improve and extend many existing results in the literature in this direction.

Convergence analysis for variational inequalities and fixed point problems in reflexive Banach spaces

Abstract: In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature.

A modified prp-cg type derivative-free algorithm with optimal choices for solving large-scale nonlinear symmetric equations

Abstract: Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiere–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with the default Newton direction. In addition, the corresponding PRP parameters are incorporated with the Li and Fukushima approximate gradient to propose two robust CG-type algorithms for finding solutions for large-scale systems of symmetric nonlinear equations. We have also demonstrated the global convergence of the suggested algorithms using some classical assumptions. Finally, we demonstrated the numerical advantages of the proposed algorithms compared to some of the existing methods for nonlinear symmetric equations.

A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

Abstract: This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

A Bregman subgradient extragradient method with self-adaptive technique for solving variational inequalities in reflexive Banach spaces

Abstract: In this paper, we introduce a self-adaptive Bregman subgradient extragradient method for solving variational inequalities in the framework of a reflexive Banach space. The step-adaptive strategy av...

New Bregman projection methods for solving pseudo-monotone variational inequality problem

Abstract: In this work, we introduce two Bregman projection algorithms with self-adaptive stepsize for solving pseudo-monotone variational inequality problem in a Hilbert space. The weak and strong convergence theorems are established without the prior knowledge of Lipschitz constant of the cost operator. The convergence behavior of the proposed algorithms with various functions of the Bregman distance are presented. More so, the performance and efficiency of our methods are compared to other related methods in the literature.

Inertial method for split null point problems with pseudomonotone variational inequality problems

Abstract: This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.

An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems

Abstract: In this paper, we study the approximation of common elements in the set of solutions of a variational inequality problem with monotone and Lipschitz continuous operator and the set of fixed points ...

A Parallel Hybrid Bregman Subgradient Extragradient Method for a System of Pseudomonotone Equilibrium and Fixed Point Problems

Abstract: We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

Convergence theorem for system of pseudomonotone equilibrium and split common fixed point problems in Hilbert spaces

Abstract: We consider a system of pseudomonotone equilibrium problem and split common fixed point problem in the framework of real Hilbert spaces. We propose a modified extragradient method with line searching technique for approximating a common element in the sets of solutions of the two nonlinear problems. The convergence result is proved without prior knowledge of the Lipschitz-like constants of the equilibrium bifunctions and the norm of the bounded linear operator of the split common fixed point problem. We further provide some application and numerical example to show the importance of the obtained results in the paper.

Inertial self-adaptive parallel extragradient-type method for common solution of variational inequality problems

Abstract: In this paper, we introduce a new inertial self-adaptive parallel subgradient extragradient method for finding common solution of variational inequality problems with monotone and Lipschitz continu...

On split equality variation inclusion problems in Banach spaces without operator norms

Abstract: The purpose of this paper is to study the approximation of solutions of split equality variational inclusion problem in uniformly convex Banach spaces which are also uniformly smooth. We introduce an iterative algorithm in which the stepsize does not require prior knowledge of operator norms. This is very important in practice because norm of operators that are often involved in applications are rarely known explicitly. We prove a strong convergence theorem for the approximation of solutions of split equality variational inclusion problem in $p$-uniformly convex Banach spaces which are also uniformly smooth. Further, we give some applications and a numerical example of our main theorem to show how the sequence values affect the number of iterations. Our results improve, complement and extend many recent results in literature.

The subgradient extragradient method for solving pseudomonotone equilibrium and fixed point problems in Banach spaces

Abstract: In this paper, we introduce a self-adaptive subgradient extragradient method for finding a common element in the solution set of a pseudomonotone equilibrium problem and set of fixed points of a qu...

Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces

Abstract: In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

A parallel viscosity extragradient method for solving a system of pseudomonotone equilibrium problems and fixed point problems in Hadamard spaces

Abstract: In this work, we study a parallel viscosity extragradient method for approximating a common solution of a finite system of pseudomonotone equilibrium problems and common fixed point problem for nonexpansive mappings in Hadamard spaces. We propose an iterative method and prove its strong convergence to an element in the intersection of the solution set of finite system of equilibrium problems and the fixed points set of nonexpansive mappings. Furthermore, we give an example in a Hadamard space which is not an Hilbert space to support the convergence theorem in the paper. This result generalizes and extends recent results in the literature.

A strong convergence halpern-type inertial algorithm for solving system of split variational inequalities and fixed point problems

Abstract: In this paper, we propose a new Halpern-type inertial extrapolation method for approximating common solutions of the system of split variational inequalities for two inverse-strongly monotone operators, the variational inequality problem for monotone operator, and the fixed point of composition of two nonlinear mappings in real Hilbert spaces. We establish that the proposed method converges strongly to an element in the solution set of the aforementioned problems under certain mild conditions. In addition, we present some numerical experiments to show the efficiency and applicability of our method in comparison with some related methods in the literature. This result improves and generalizes many recent results in this direction in the literature.

Modified projected subgradient method for solving pseudomonotone equilibrium and fixed point problems in Banach spaces

Abstract: Motivated by the work of D.V. Hieu and J.-J. Strodiot [Strong convergence theorems for equilibrium problems and fixed point problems in Banach spaces, J. Fixed Point Theory Appl., (2018), 20:131], we introduce a new projected subgradient method for solving pseudomonotone equilibrium and fixed point problem in Banach spaces. The main iterative steps in the proposed method use a projection method and do not require any Lipschitz-like condition on the equilibrium bifunction. A strong convergence result is proved under mild conditions and we applied our algorithm to solving pseudomonotone variational inequalities in Banach spaces. Also, we provide some numerical examples to illustrate the performance of the proposed method and compare it with other methods in the literature.

An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces

Abstract: In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove a convergence result for solving the equilibrium problem without any prior estimate of the Lipschitz-like constants of the bifunction. Furthermore, we provide some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. This result improves and extends many recent results in this direction in the literature.

Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces

Abstract: In this paper, using the concept of Bregman distance, we introduce a new Bregman subgradient extragradient method for solving equilibrium and common fixed point problems in a real reflexive Banach space. The algorithm is designed, such that the stepsize is chosen without prior knowledge of the Lipschitz constants. We also prove a strong convergence result for the sequence that is generated by our algorithm under mild conditions. We apply our result to solving variational inequality problems, and finally, we give some numerical examples to illustrate the efficiency and accuracy of the algorithm.