A simple smooth exact penalty function for smooth optimization problem

For smooth optimization problem with equality constraints, new continuously differentiable penalty function is derived. It is proved exact in the sense that local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function under some nondegeneracy assumption. It is simple in the sense that the penalty function only includes the objective function and constrained functions, and it doesn't include their gradients. This is achieved by augmenting the dimension of the program by a variable that controls the weight of the penalty terms.