Factorization of Minty and Stampacchia variational inequality systems

On Maingé’s Approach for Hierarchical Optimization Problems

“…The concept of variational inequalities plays an important role in various kinds of problems in pure and applied sciences (see, for example, [1][2][3][4][5][6][7][8][9][10]). Moreover, the rapid development and the prolific growth of the theory of variational inequalities have been made by many researchers.…”

Iterative algorithm for a system of variational inclusions involving H-accretive operators in Banach spaces

“…Recently, some new and interesting problems related to variational inequalities were studied in the papers [3,4,15,16,23,24]. They are systems of variational inequalities consisting of a family of variational inequalities.…”

“…In [15], Kassay and Kolumbán introduced a system of variational inequalities and proved an existence theorem by the Ky Fan lemma. In [16], Kassay, Kolumbán and Páles studied Minty and Stampacchia variational inequality systems with the help of the Kakutani-Fan-Glicksberg fixed point theorem. The study of systems of variational inequalities is interesting and important because of the known fact that a Nash equilibrium point can be found by the solution for a family of variational inequalities (see [14,20]).…”

Some Existence and Convergence Theorems for Solving a System of Hierarchical Optimization Problems

“…(VI) In (1.9), if T i = P K i for each i = 1, 2, then the bi-level hierarchical optimization problem (1.9) reduces to a bi-level optimization problem [28][29][30]: find (x ⇤ , y ⇤ ) 2 K 1 ⇥ K 2 such that 8 <…”