A New Smoothing Nonlinear Penalty Function for Constrained Optimization

Abstract

Abstract:In this study, a new smoothing nonlinear penalty function for constrained optimization problems is presented. It is proved that the optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, we develop an algorithm for finding an optimal solution of the optimization problems with inequality constraints. We further discuss the convergence of this algorithm and test this algorithm with three numerical examples. The numerical examples show that the proposed algorithm is feasible and effective for solving some nonlinear constrained optimization problems.

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

“…Numerical results obtained by both of our algorithms are much better than the results in [14] and find the correct solutions as in [15]. Further, it can be seen that the approximate solutions obtained by our algorithms with the lower iteration numbers in comparison with the [14].…”

“…In [14], the obtained global solution is x * = (2.3295, 3.1784) with objective function value f (x * ) = −5.5080. In the paper [15], the obtained approximate optimal solution is x * = (2.112103, 3.900086) with objective function value f (x * ) = −6.012190.…”

A new perturbed smooth penalty function for inequality constrained optimization

“…In [21], the obtained global solution is x * = (2.3295, 3.1784) with objective function value f(x * ) = −5.5080. In the paper [22], the obtained approximate optimal solution is x * = (2.112103, 3.900086) with objective function value f(x * ) = −6.012190. Numerical results obtained by our algorithm are much better than the results in [21] and find the correct solutions as in [22].…”

Smoothing of Mammogram Using an Improved Gradient based Technique

“…The value of βmax is 1.0e 5 . The quadratic equation involves large matrix inversion [18] and can be computed using Fast Fourier Transform (FFT) [19] for fast computation.…”