Quasi-Newton methods are among the most practical and efficient iterative methods for solving unconstrained optimization problem . These methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. Among those Quasi-Newton methods we focus on two different update formulas, which use line search strategy to find step length in each iteration. We call these methods Quasi-Newton line search methods, namely DFP and BFGS and applied this method over unconstrained non -linear least square problem. BFGS is well-liked for its efficiency and self-correcting properties to solve unconstrained non-linear least square optimization problem.

Keywords: Quasi-Newton-equation, Line Search, Wolfe conditions, Step length, Hessian Matrix formula, unconstrained non-linear optimization problem,