A Smooth Penalty Function Algorithm for Computing Nonlinear Inequality Constraint Optimization Problem

• Published in: Mathematical problems in engineering Vol. 2024; no. 1
• Main Authors: Singh, Dharminder, Singh, Amanpreet, Singh, Amrit Pal, Garg, Rachit, Prashar, Deepak, Khan, Arfat Ahmad, Yimam, Frie Ayalew
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.01.2024
• Subjects: Algorithms; Lagrange multiplier; Methods; Optimization; Penalty function; Smoothing
• ISSN: 1024-123X; 1026-7077; 1563-5147; 1563-5147
• DOI: 10.1155/2024/1224408

Functions in nonlinear programing optimization are sometimes not easily differentiable. When such kinds of functions are present in the optimization problem, then the process of obtaining the solution can sometimes become quite lengthy. Traditional and classical methods cannot be used to solve such optimization problems because such methods assume the functions to be differentiable. Smoothing of nondifferentiable functions is thus required to tackle such difficulties. In this study, we introduce the concept of constructing a technique to smooth such nondifferentiable functions. We begin with the smoothing of the penalty function. On the basis of it, we come up with an algorithm to find the best way to solve an optimization problem with inequality constraints. We also talk about how to figure out the error for a certain smooth penalty function. We also provide numerical examples to demonstrate that the suggested approach is practical and usable.