Perturbed smoothing approach to the lower order exact penalty functions for nonlinear inequality constrained optimization

In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Error estimations between smoothed penalty function and nonsmooth penalty function are investigated. By using these new smooth penalty functions, a nonlinear optimization problem with inequality constraints is converted into a sequence of minimizations of continuously differentiable function. Then based on each of the smoothed penalty functions, we develop an algorithm respectively to finding an approximate optimal solution of the original constrained optimization problem and prove the convergence of the proposed algorithms. The effectiveness of the smoothed penalty functions is illustrated through three examples, which show that the algorithm seems efficient.