On the modified conjugate-descent method and its $q$-variant for unconstrained optimization problems

Abstract

Based upon the conjugate-descent(CD) conjugate gradient methods(CGMs),  we first provide the modified conjugate-descent (MCD) scheme, that is, the modification to the denominator terms of original CD scheme. Then we apply $q$-calculus to MCD to establish its $q$-variant. Whether the line search technique is exact or not, the two methods can generate decent directions at every iteration. Under appropriate assumptions and standard Wolfe line search technique, the presented methods are proven to be globally convergent. Numerical experiments demonstrate the offered methods are efficient.