An Improved Secant Type Method for Solving Nonlinear Optimization Problems

Abstract

This project introduces an improved version of the Modern secant- kind method for solving nonlinear optimization problems. Steffensen’s method is used to generate the initial approximation, eliminating the need for second derivative calculations and improving computational efficiency. Numerical results obtained from seven test problems demonstrate that the proposed method converges faster with fewer iterations and requires less computational time compared to Newton’s method and the Modern secant-kind method.

AMS Subject Classification: 65K05, 65H05

Keywords: Nonlinear optimization, Newton’s method, Secant method, Steffensen’s method, Modern secant-kind method.