A new gradient method via quasi-Cauchy relation whichguarantees descent

摘要

We propose a new monotone algorithm for unconstrained optimization in the frame ofBarzilai and Borwein (BB) method and analyze the convergence properties of this newdescent method. Motivated by the fact that BB method does not guarantee descent in theobjective function at each iteration, but performs better than the steepest descent method,we therefore attempt to find stepsize formula which enables us to approximate the Hessianbased on the Quasi-Cauchy equation and possess monotone property in each iteration.Practical insights on the effectiveness of the proposed techniques are given by a numericalcomparison with the BB method.