Iterative proximal regularization of a modified Lagrangian functional for solving a semicoercive model problem with friction

A problem of unconstrained minimization of a semicoercive nondifferentiable functional corresponding to a model friction problem is reduced to a problem of constrained minimization of a differentiable functional. An algorithm based on an iterative proximal regularization of a modified Lagrangian functional is used for solving the problem thus obtained. Convergence of a finite element solution is investigated. The results of numerical calculation are presented.