Some new step-size rules for optimization problems
The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f + 1/2(x - xk)TBk(x - xk) was used as the merit function in iteration k,where Bκ is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.