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

Based upon the conjugate-descent (CD) method in conjugate gradient methods (CGMs), we first propose a modified conjugate-descent (MCD) scheme, which adjusts the denominator terms of original CD scheme. Next, we apply q-calculus to the MCD method to derive its q-variant. Regardless of whether the line search technique is exact or not, both methods guarantee descent directions at every iteration. Under appropriate assumptions and the standard Wolfe line search technique, the presented methods are proven to be globally convergent. Numerical experiments demonstrate that the offered methods are efficient.