Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems

Abstract

Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities problems in real Hilbert space. The result of the strong convergence of the method is well established without the information of the operator’s Lipschitz constant. There are proper mathematical studies relating our newly designed method to the currently state of the art on several practical test problems.

Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications

“…Many authors established and generalized several results on the existence and nature of the solution of the equilibrium problems (see for more detail [1,4,5]). Due to the importance of this problem (EP) in both pure and applied sciences, many researchers studied it in recent years [6][7][8][9][10][11][12][13][14][15][16][17] and other in [18][19][20][21][22]. Tran et al in [23] introduced iterative sequence {u n } in the following way:…”

An inertial parallel CQ subgradient extragradient method for variational inequalities application to signal-image recovery

“…However, the convergence of this method requires slightly strong assumptions that operators are strongly monotone or inverse strongly monotone. Many algorithms have been proposed and studied for solving VIP(1) of these algorithms involve projection methods [5,6,10,11,39,40,43,46,47,51]. The VIP(1) serves as a powerful mathematical tool and generalizes many mathematical methods, in the sense that, it includes many special problems [29] such as convex feasibility problems, linear programming problem, minimizer problem, saddle -point problems, Hierarchical variational inequality problems.…”

Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems

“…The first well-known projection method is the gradient projection method that is used to solve variational inequalities. Moreover, several other projection methods have been established including the well-known extragradient method [18] the subgradient extragradient method [4,5] and others in [6,26,20,30,11] and others in [22,7,23,14,9,27,28,2,1,10]. The above numerical techniques are used to examine the variational inequalities involving monotone, strongly monotone, or inverse monotone.…”