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...

The correction equation in the Jacobi-Davidson method is effective in a subspace orthogonal to the current eigenvector approximation, while for the continuation of the process only vectors orthogonal to the search subspace are of importance. Such a vector is obtained by orthogonalizing the (approximate) solution of the correction equation against the search subspace. As an alternative, a varian...

It has long been known that the gradient (steepest descent) method may fail on nonsmooth problems, but the examples that have appeared in the literature are either devised specifically to defeat a gradient or subgradient method with an exact line search or are unstable with respect to perturbation of the initial point. We give an analysis of the gradient method with steplengths satisfying the A...

New accelerated nonlinear conjugate gradient algorithms which are mainly modifications of the Dai and Yuan’s for unconstrained optimization are proposed. Using the exact line search, the algorithm reduces to the Dai and Yuan conjugate gradient computational scheme. For inexact line search the algorithm satisfies the sufficient descent condition. Since the step lengths in conjugate gradient algo...

This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of new that it considers problems special triangular number. For this purpose, quantities are transformed into membership and non-membership parametric forms, a line procedure emplo...

Waste management problems are subject to uncertainties presented as intervals, random variables and/or fuzzy sets. During the past 20 years, inexact programming methods have been developed and applied increasingly to waste management problems under uncertainty. To obtain a snapshot of these studies, this paper gives a review on recent developments, applications, challenges, and barriers associa...

Internet search engines have become an indispensable part of everyday living and business today. Although the capabilities of Internet search engines are incrementally improving steadily, it may be time for us to explore a few new directions that can take the search engines to the next level. In this article, we will summarize the current activities in advancing the state of Internet search eng...

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...