A modified predictor–corrector algorithm for solving nonconvex generalized variational inequality

Abstract

In this paper, we suggest and analyze a new modified predictor-corrector algorithm for solving a nonconvex generalized variational inequality using the auxiliary principle technique; the convergence of the algorithm requires the partially relaxed strong monotonicity of the operator.

Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets

“…However, in fact, the convexity assumption may not be required, because the algorithm may be well defined even if the considered set is nonconvexs (e.g., when the considered set is a closed subset of a finite dimensional space or a compact subset of Hilbert space, etc.) see [1,4,20,25,26,27]. While, it may be from the practical point of view, one may see that the nonconvex problems are more useful and general than convex case, subsequently, now many researchers are convinced and paid attention to many nonconvex cases.…”

Two Step Algorithm for Solving Regularized Generalized Mixed Variational Inequality Problem

“…Very recently, Bounkhel et al [4], Noor [13], Moudafi [10], and Pang et al [14] have considered the variational inequality problems and equilibrium problems over these nonconvex sets. They suggested and analyzed some projection type iterative algorithms by using the prox-regular technique and auxiliary principle technique.…”

“…We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly θ-pseudomonotonicity. The theorems presented in this paper represent improvement and generalization of the previously known results for solving equilibrium problems and variational inequality problems involving the nonconvex (convex) sets, see for example Noor [13], Pang et al [14], and Xia and Ding [19]. …”

Generalized System of Variational Inequalities in Banach Spaces

“…Variational inequality and complementarity problems are of fundamental importance in a wide range of mathematical and applied sciences problems, such as mathematical programming, traffic engineering, economics and equilibrium problems, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The ideas and techniques of the variational inequalities are being applied in a variety of diverse areas of sciences and proved to be productive and innovative.…”