Steepest descent: Steepest descent algorithms take incremental steps downhill. These include many of the direct search algorithms as well as some gradient-based (Cauchy’s sequential line search and ...

Mathematics of Operations Research, Vol. 12, No. 4 (Nov., 1987), pp. 678-699 (22 pages) We consider generalizations of the steepest descent algorithm for solving asymmetric systems of equations. We ...

Conjugate gradient methods form a class of iterative algorithms that are highly effective for solving large‐scale unconstrained optimisation problems. They achieve efficiency by constructing ...

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of ...