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 …

This paper focuses on computing the convex conjugate operation that arises when solving
Euclidean Wasserstein-2 optimal transport problems. This conjugation, which is also …

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale
unconstrained optimization problems. The search direction at each iteration of the algorithm …

The BFGS method, which has great numerical stability, is one of the quasi-Newton line
search methods. However, the global convergence of the BFGS method with a Wolfe line …

In this paper, an extended nonmonotone line search is proposed to improve the efficiency of
the existing line searches. This line search is first proved to be an extension of the classical …

In this paper, a new nonmonotone line search rule is proposed, which is verified to be an
improved version of the nonmonotone line search technique proposed by Zhang and Hager …

We present a modification of the limited memory BFGS (L-BFGS) method that ensures global
and linear convergence on nonconvex objective functions. Importantly, the modified method …

In this work, a new advanced active set limited memory BFGS (Broyden–Fletcher–Goldfarb–
Shanno) algorithm is proposed for efficiently training weight-constrained neural networks …

Abstract The Quasi-Newton method is one of the most effective methods using the first
derivative for solving all unconstrained optimization problems. The Broyden family method …

An effective hybrid algorithm is proposed for solving multiobjective optimization engineering
problems with inequality constraints. The weighted sum technique and BFGS quasi …