Linesearch methods for bilevel split pseudomonotone variational inequality problems

Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints

“…x 1 −x 0 ≤ TOL, where the parameters are given in the following: α n = 1 5n−1 , ε n = 1 (5n−1) 2 , ρ n = 1 5 , λ n = 1 N , β n = 1 2 , θ n =θ n . For TOL= 10 −5 , N = 4, x 0 = (1, 2, 3, 4), and x 1 = (5,6,7,8), the approximate solution obtained after 319 iterations is…”

“…Usually, (1) is called the upper level problem and (2) is called the lower level problem. Many real life problems can be modeled as a bilevel problem and some studies have been performed towards solving different kinds of bilevel problems using approximation theory-see, for example, for bilevel optimization problem [1][2][3], for bilevel variational inequality problem [4][5][6][7][8][9], for bilevel equilibrium problems [10][11][12], and [13,14] for its practical applications. In [14], application of bilevel problem (bilevel optimization problem) in transportation (network design, optimal pricing), economics (Stackelberg games, principal-agent problem, taxation, policy decisions), management (network facility location, coordination of multi-divisional firms), engineering (optimal design, optimal chemical equilibria), etc.…”

Proximal Gradient Method for Solving Bilevel Optimization Problems

“…The problem is also called the leader's and follower's problem where the problem (5) is called the leader's problem and (6) is called the follower's problem, meaning, the first player (which is called the leader) makes his selection first and communicates it to the second player (the so-called follower). There are many studies for several type bilevel problems, see, for example, [15,[17][18][19][20][21][22][23][24]. The bilevel optimization problem is a bilevel problem when the hierarchical structure involves the optimization problem.…”

Two inertial linesearch extragradient algorithms for the bilevel split pseudomonotone variational inequality with constraints

“…Inspired by the results presented in [2], we introduce two modified inertial linesearch extragradient algorithms for finding a solution of the BSVIP with a fixed-point constraint. Our proposed algorithms are based on the inertial method, the linesearch extragradient method, the hybrid steepest-descent method, and the viscosity approximation method.…”