In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...

A tolerant derivative–free nonmonotone line search technique is proposed and analyzed. Several consecutive increases in the objective function and also non descent directions are admitted for unconstrained minimization. To exemplify the power of this new line search we describe a direct search algorithm in which the directions are chosen randomly. The convergence properties of this random metho...

This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although some prior work has established convergence results for algorithms that integrate both descent and negative curvature directions, there has not yet been numerical evidence showing that such methods offer significant performance improvements. In thi...

Recently, important contributions on convergence studies of conjugate gradient methods have been made by Gilbert and Nocedal [6]. They introduce a “sufficient descent condition” to establish global convergence results, whereas this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, [6] hints that the sufficient descent condition, which was enforced by their ...

We introduce a new optimization strategy to compute numerical approximations of minimizers for optimal control problems governed by scalar conservation laws in the presence of shocks. We focus on the 1 − d inviscid Burgers equation. We first prove the existence of minimizers and, by a Γ-convergence argument, the convergence of discrete minima obtained by means of numerical approximation schemes...

In this paper, we evaluate the performance of a new class of conjugate gradient methods for training recurrent neural networks which ensure the sufficient descent property. The presented methods preserve the advantages of classical conjugate gradient methods and simultaneously avoid the usually inefficient restarts. Simulation results are also presented using three different recurrent neural ne...

In this paper, a new conjugate conjugate method with sufficient descent property is proposed for the unconstrained optimization problem. An attractive property of the new method is that the descent direction generated by the method always possess the sufficient descent property, and this property is independent of the line search used and the choice of ki  . Under mild conditions, the global c...