Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization.

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent condition g(k)(T)d(k) <= -(1 - 1/4 theta(k))) parallel to g(k)parallel to(2) (theta(k) > 1/4) and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large- scale unconstrained optimization.