A Smooth Penalty Framework for Solving Nonlinear Inequality-Constrained Optimization Problems

Abstract

We propose a smooth approximation of the exact l1 penalty function. This paper presents a novel
smooth penalty function designed to address nonlinear programming problems with inequality-constrained.
With help of this formulation, an algorithm is developed, and its convergence is rigorously established. The
proposed method is tested on two numerical examples to demonstrate its effectiveness, with results com-
pared against those obtained from existing algorithms. The findings demonstrate that the proposed approach
provides reliable convergence and competitive performance for solving these types of optimization problems.