This book is on conjugate gradient methods for unconstrained optimization. The concept of
conjugacy was introduced by Magnus Hestenes and Garrett Birkhoff in 1936 in the context of …

It is efficient to use the Hestenes–Stiefe (HS) conjugate gradient algorithm in solving large-
scale complex smooth optimization problems because of its simplicity and low calculation …

A new efficient random search algorithm is introduced for solving inversion problems in
geophysical studies. The proposed algorithm is inherently a stochastic optimization method …

Geophysical inverse problems are commonly ill-posed and require proper regularization to
gain acceptable solutions. Adopting constraints on the smoothness and/or specified …

In this paper we propose the use of damped techniques within Nonlinear Conjugate
Gradient (NCG) methods. Damped techniques were introduced by Powell and recently …

In this paper, we deal with matrix-free preconditioners for nonlinear conjugate gradient
(NCG) methods. In particular, we review proposals based on quasi-Newton updates, and …

Extension of the main grid to remote areas is economically not feasible. To electrify remote
areas, one of the best choices is to install Renewable Energy Sources (RES) as a distributed …

In this paper we consider the issue of computing negative curvature directions, for
nonconvex functions, within Newton-Krylov methods for large scale unconstrained …

In this paper we consider the issue of computing negative curvature directions, for
nonconvex functions, within Newton–Krylov methods for large scale unconstrained …

The secant equation traditionally constitutes the basis of quasi-Newton methods, as the
updated Hessian approximations satisfy the equation on each iteration. Modified versions of …