Manuscript Title:

ENHANCED VARIABLE REDUCTION TECHNIQUES FOR SOLVING NONLINEAR EQUALITY-CONSTRAINED OPTIMIZATION PROBLEMS

Author:

Dr. VIPIN KUMAR, Dr. SACHIN KUMAR AGARWAL

DOI Number:

DOI:10.5281/zenodo.16308877

Published : 2025-07-23

About the author(s)

1. Dr. VIPIN KUMAR - Department of Mathematics, Faculty of Engineering, Teerthanker Mahaveer University, Moradabad, India.
2. Dr. SACHIN KUMAR AGARWAL - Department of Applied Sciences & Humanities, Moradabad Institute of Technology, Moradabad, India.

Full Text : PDF

Abstract

This paper presents an enhanced methodology for solving nonlinear equality-constrained optimization problems using variable reduction algorithms. The core idea is to locally convert the constrained model into an unconstrained subspace, thereby simplifying computation. Special focus is given to both smooth and non-smooth functions. The approach leverages second-order approximations and to ensure convergence. We develop updated formulations, provide a numerical example, and support findings with a graphical representation. The results demonstrate the potential of variable reduction techniques in improving computational efficiency and accuracy in complex optimization tasks.


Keywords

Lagrangian Functions, Jacobian, Hessian Function, Multi-objective Functions, Non-Linear Function, Optimization Technique, Newton Method.