Abstract
A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the methods used to solve equilibrium problems involve iterative methods, which is why the aim of this article is to establish a new iterative method by incorporating an inertial term with a subgradient extragradient method to solve the problem of equilibrium, which includes a bifunction that is strongly pseudomonotone and meets the Lipschitz-type condition in a real Hilbert space. Under certain mild conditions, a strong convergence theorem is proved, and a required sequence is generated without the information of the Lipschitz-type cost bifunction constants. Thus, the method operates with the help of a slow-converging step size sequence. In numerical analysis, we consider various equilibrium test problems to validate our proposed results.
Highlights
Assume that a bifunction f : H × H → R satisfying the conditions f (v, v) = 0 for each v ∈ K.A equilibrium problem [1,2] for f on K is said to be: Find v∗ ∈ K such that f (v∗, v) ≥ 0, ∀ v ∈ K. (1)where K is a non-empty closed and convex subset of a Hilbert space H
We set up a new method by combining an inertial term with an extragradient method for solving a family of strongly pseudomonotone equilibrium problems
Numerical experiments clearly point out that the method with an inertial term performs better than those without an inertial term
Summary
The above well-defined simple mathematical problem (1) includes many mathematical and applied sciences problems as a special case, consisting of the fixed point problems, vector and scalar minimization problems, problems of variational inequalities (VIP), the complementarity problems, the Nash equilibrium problems in non-cooperative games, and inverse optimization problems [1,4,5]. This problem is seen as a problem of Ky Fan inequality based on his initial contribution [2].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
