Optimal control of a non-smooth quasilinear elliptic equation

This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation nonlinear coefficient in the principal part that locally Lipschitz continuous and directionally but not G\^ateaux differentiable. leads to control-to-state operator differentiable as well. Based on suitable regularization scheme, we derive C- strong stationarity conditions. Under additional assumption nonlinearity PC^1 function countably many points of nondifferentiability, show both conditions are equivalent. Furthermore, under this relaxed optimality system amenable numerical solution using semi-smooth Newton method. illustrated examples.