Inertial Subgradient Projection Algorithms Extended to Equilibrium Problems

A Projection Subgradient Algorithm for Finding a Common Solution of Equilibrium and Fixed Point Problems

“…As an illustration, we apply Algorithm 3.1. to solve the well-known Nash-Cournot oligopolistic market equilibrium model with equilibrium constraint in [9]. Consider a class of well-known problem oligopolistic market equilibrium problem Nash-Cournot between n firms in the space R n .…”

“…Obviously, if F : R n → R n is pseudomonotone, L-Lipschitz continuous and g : R n → R is convex, differentiable then the function f (x, y) satisfies assumptions A 1 , A 2 , A 4 . We now consider the case that the function p j (δ x ) is affine p j (δ x ) = α j − β j δ x , β j ≥ 0, α j ≥ 0, ∀j = 1, ..., n. Then F j (x) = −p j (δ x ) − x j p j (δ x ) = β j δ x − α j + β j x j = 2β j x j + β j n j=1,j =i It is known that B is a positive symmetric matrix and F is monotone and B -Lipschitz continuous ( [9]). Therefore, this model can be solve by Algorithm 3.1.…”

A novel method for solving nonmonotone equilibrium problems

“…These methods often require the convexity on the second variable and the monotonicity or generalized monotonicity of the bifunction f . Up to now, several results have been achieved for this class of equilibrium problems (see papers [1,13,22,29,32] and books [2,16]). Recently, J. Strodiot et al in [28] (see also [7,9,15]) have introduced shrinking projection algorithms to solve nonmonotone equilibrium problems.…”