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