This paper investigates the potential behavior, both good and bad, of the well-known BFGS algorithm for smooth minimization, when applied to nonsmooth functions. We consider three very particular examples. We first present a simple nonsmooth example, illustrating how BFGS (in this case with an exact line search) typically succeeds despite nonsmoothness. We then study, computationally, the behav...

We study the numerical performance of a limited memory quasi-Newton method for large scale optimization, which we call the L-BFGS method. We compare its performance with that of the method developed by Buckley and LeNir (1985), which combines cyles of BFGS steps and conjugate direction steps. Our numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and...

To make glowworm swarm optimization (GSO) algorithm solve multi-extremum global optimization more effectively, taking into consideration the disadvantages and some unique advantages of GSO, the paper proposes a hybrid algorithm of Broyden–Fletcher–Goldfarb– Shanno (BFGS) algorithm and GSO, i.e., BFGS-GSO by adding BFGS local optimization operator in it, which can solve the problems effectively ...

L-BFGS has been applied as an effective parameter estimation method for various machine learning algorithms since 1980s. With an increasing demand to deal with massive instances and variables, it is important to scale up and parallelize L-BFGS effectively in a distributed system. In this paper, we study the problem of parallelizing the L-BFGS algorithm in large clusters of tens of thousands of ...

This paper is aimed to extend a certain damped technique, suitable for the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, to the limited memory BFGS method in the case of the large-scale unconstrained optimization. It is shown that the proposed technique maintains the global convergence property on uniformly convex functions for the limited memory BFGS method. Some numerical results are descri...