Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators

System of Generalized Nonlinear Regularized Nonconvex Variational Inequalities

“…In recent years, several authors studied different type of systems of variational inequalities and suggested iterative algorithms to find the approximate solutions of such system (see [3,6,9,11,14,19,20]). We remark that the almost all results concerning the system of solutions of iterative scheme for solving the system of variational inequalities and related problems are being considered in the setting of convex sets.…”

System of implicit nonconvex variationl inequality problems A projection method approach

“…In recent years, Bounkhel et al [6], Moudafi [20], Wen [28], Kazmi et al [17], Noor [[23, 24, 22] and the relevant references cited therein], Alimohammady et al [1], Balooee et al [4] suggested and analyzed iterative algorithms for solving some classes (systems) of nonconvex variational inequality problems in the setting of uniformly prox-regular sets.…”

“…SINVIP is different from those considered in [1,4,6,16,20,22,23,24,28] and includes the new and known systems of nonconvex (convex) variational inequality problems as special cases. Using the properties of projection operator over uniformly prox-regular sets, we suggest some iterative algorithms for finding the approximate solution of SINVIP and its an important special case.…”

Convergence analysis of projection methods for a new system of general nonconvex variational inequalities

“…It has been shown that variational inequalities provide the most natural, direct, simple, and efficient framework for a general treatment of some unrelated problems arising in various fields of pure and applied sciences. In recent years, there have been considerable activities in the development of numerical techniques including projection methods, Wiener-Hopf equations, auxiliary principle, and descent framework for solving variational inequalities; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein. These activities have motivated us to generalize and extend the variational inequalities and related optimization problems in several directions using novel techniques.…”

“…On the other hand, Verma [13] and Noor and Noor [14] proposed explicit projection methods for solving systems of variational inequalities and general variational inequalities on a closed convex subset of Hilbert space, respectively. Very recently, Wen [15] modified projection methods to a generalized system of nonconvex variational inequalities with different nonlinear operators. However, only iterative sequences {g(x n )}, {g(y n )} come from the projection methods, which requires that mapping g must be injective in order to arrive at a solution of the generalized system.…”