For a rather general optimization problem, which covers Bingham flow problems, image restoration problems, obstacle problems (here: two-sided and with a gradient operator), Signorini problems for contact problems in elasticity, friction problems, fitting problems (with \(p\)-norm, \(p=1\)) and optimal control problems, the authors study augmented Lagrange techniques using Yosida approximation and prove optimality conditions and convergence results. They apply their new results to the above mentioned examples. Finally, they propose an active set strategy based on the above used regularized optimality system and prove “finite” convergence properties.