A smoothing approximation method for classical l1 exact penalty function for optimization problems.

The given manuscript deals with the development of a new smoothing technique for approximation of non- derivable l1 exact penalty functions for an optimization problem which is constrained in nature. The optimal solution of the problem framed from the original optimization problem as a smoothening optimization problem is proved to be identical to the original problem. Error estimation is done for smooth penalty problem, non-smooth penalty problem, and for the original problem. A procedure is developed to solve the constrained optimization problem consigned on the smoothing technique proposed in the paper. The convergence behaviour of the proposed procedure is also studied under soft conditions.