A novel class of exact penalty function approach for optimization problems with inequality constraints

Nonlinear programming has always had an important place in the literature, from the past to the present. This study aims to solve the continuous constrained optimization problem, which is an important subclass of nonlinear programming problems. A new twice differentiable smoothing technique for exact penalty functions is presented. It has been demonstrated that any optimum solution of the smoothed exact penalty function coincides with an optimal solution of the original problem. Error analysis is carried out to demonstrate that the optimal solution of the smoothed exact penalty problem approximates to an optimal solution to the constrained optimization problem. The proposed smoothing technique is used to develop an algorithm that produces an optimal solution for the constrained optimization problem. The convergence of the method is demonstrated based on both theoretical and numerical considerations. Numerical examples are provided to illustrate the effectiveness of the proposed method.

کلیدواژه ها:

Constrained optimization ، Smoothing technique ، Exact penalty function