Homotopy method for solving mathematical programs with bounded box-constrained variational inequalities

Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators

“…Equilibrium problems have been studied extensively in the literature (see, e.g., [2][3][4][5]). Many problems, such as variational inequalities [6][7][8][9][10][11][12][13][14][15], fixed point problems [16][17][18][19][20][21], and Nash equilibrium in noncooperative games theory [1,22], can be formulated in the form of Equation (3).…”

Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

“…This notion, that mainly involves some important operators, plays a key role in applied mathematics, such as obstacle problems, optimization problems, complementarity problems as a unified framework for the study of a large number of significant real-word problems arising in physics, engineering, economics and so on. For more information, the reader can refer to [1][2][3][4][5][6][7][8][9][10][11][12]. For solving VI (1) in which the involved operator f may be monotone, several iterative algorithms have been introduced and studied, see, e.g., [13][14][15][16][17][18].…”

Split Systems of Nonconvex Variational Inequalities and Fixed Point Problems on Uniformly Prox-Regular Sets

“…On the other hand, over the past three decades, there has been quite an activity in the development of powerful and highly efficient numerical methods to solve the VIP and its applications [12][13][14][15][16][17][18]. There is a substantial number of methods, including the linear approximation method [19,20], the auxiliary principle [21,22], the projection technique [9,11], and the descent framework [23]. For applications, numerical techniques and other aspects of variational inequalities and split problems, please see [19,20,[24][25][26][27][28].…”

“…There is a substantial number of methods, including the linear approximation method [19,20], the auxiliary principle [21,22], the projection technique [9,11], and the descent framework [23]. For applications, numerical techniques and other aspects of variational inequalities and split problems, please see [19,20,[24][25][26][27][28].…”