Development of The Steepest Descent Method for Unconstrained Optimization of Nonlinear Function

The q-gradient method used a Yuan step size for odd steps, and geometric recursion as an even (q-GY). This study aimed to accelerate convergence minimum point by minimizing the number of iterations, dilating parameter q independent variable then comparing results with three algorithms namely, classical steepest descent (SD) method, Steps (SDY), (q-G). numerical were presented in tables graphs. Rosenbrock function f(x)=〖(1-x_1)〗^2+100〖(x_2-〖x_1〗^2)〗^2 determined μ=1,σ_0=0.5,β=0.999, starting (x_0) uniform distribution on interval x_0= (-2.048, 2.048) R^2, 49 points executed using Python online compiler 64bit core i3 laptop. maximum iterations was 58,679. Using tolerance limits stopping criteria is 10-4 inequality 〖f(x〗^*)>f get results. q-GY down ward movement towards better than SD SDY methods while showed good enough performance increase