Search Based On New Quasi-Newton Equation Improved Unconstrained Filter Line

Line search method is traditionally a simple, easy, effective and reliable optimization method. When used the line search method to solve optimization problems, the key points are to find descent direction and step size. In this paper, our algorithm is set up by considering both search direction and step size. For the search direction, we use tensor method modify the Zhang’s quasi-Newton equation, and get our new quasi-Newton equation with function value information, which is more precise and wider than Zhang’s in approximation to Hessian of an objective function. We construct a type of descent direction of BFGS formula on this new quasi-Newton equation. For the step size, we adjust step size αk by backtracking method and fix the value αk by our modified filter acceptance criteria (depending on the descent direction with function value information). Our new algorithm is produced by applying this descent direction and step size to line search. Under reasonable assumptions, the convergence of the algorithm is proved. Numerical experiments show effective the improved algorithm of unconstrained filter line search on the basis of new quasi-Newton equation.