Simultaneous distributed-boundary optimal control problems driven by nonlinear complementarity systems

The primary goal of this paper is to study a nonlinear complementarity system (NCS, for short) with and nonhomogeneous partial differential operator mixed boundary conditions, simultaneous distributed-boundary optimal control problem governed by (NCS), respectively. First, we formulate the weak formulation (NCS) variational inequality double obstacle constraints (MVI, short), prove existence uniqueness solution (MVI). Then, power penalty method applied introducing an approximating without (AMVI, short). After that, convergence result that unique (MVI) can be approached (AMVI) when parameter tends infinity, established. Moreover, explore solvability described (MVI), consider family problems driven (AMVI). Finally, provide on asymptotic behavior controls, states minimal values problems.