new conjugacy condition with pair-conjugate gradient methods for unconstrained optimization

Abstract

ABSTRACTConjugate gradient methods are wildly used for unconstrainedoptimization especially when the dimension is large. In this paper wepropose a new kind of nonlinear conjugate gradient methods which on thestudy of Dai and Liao (2001), the new idea is how to use the pair conjugategradient method with this study (new cojugacy condition) which consider aninexact line search scheme but reduce to the old one if the line search isexact. Convergence analysis for this new method is provided. Our numericalresults show that this new methods is very efficient for the given ten testfunction compared with other methods.