An efficient hybrid bfgs-cg search direction for solving unconstrained optimization problems

Abstract

Recently, various methods for solving unconstrained optimization problems have been proposed. Most of these methods employ different approach to calculate the search direction dĸ . Some of the famous search direction includes, Newton method, Quasi Newton method, and Conjugate Gradient method (CG). In thispaper,wedevelopanewhybridmethod which uses CG and BFGS search direction simultaneously under strong Wolfe line search. Various Numerical results have been presented to illustrate the efficiency of the proposed method when comparedwithCGandBFGSmethod.UnderstrongWolfelinesearch,we show that our new algorithm convergesglobally.