  In this work, we study the distributed Nash equilibrium seeking problem for
monotone generalized noncooperative games with set constraints and shared
affine inequality constraints. A distributed regularized penalty method is
proposed. The idea is to use a differentiable penalty function with a
time-varying penalty parameter to deal with the inequality constraints. A
time-varying regularization term is used to deal with the ill-poseness caused
by the monotonicity assumption and the time-varying penalty term. The
asymptotic convergence to the least-norm variational equilibrium of the game is
proven. Numerical examples show the effectiveness and efficiency of the
proposed algorithm.
