Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization

Abstract

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just $O(n)$. Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.