Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our a...

In this paper, it is aimed to computationally conduct a performance benchmarking for the steepest descent and three well-known conjugate gradient methods (i.e., Fletcher-Reeves, Polak-Ribiere Hestenes-Stiefel) along with six different step length calculation techniques/conditions, namely Backtracking, Armijo-Backtracking, Goldstein, weakWolfe, strongWolfe, Exact local minimizer in unconstrained...

In this paper, we make a modification to the LS conjugate gradient method and propose a descent LS method. The method can generates sufficient descent direction for the objective function. We prove that the method is globally convergent with an Armijo-type line search. Moreover, under mild conditions, we show that the method is globally convergent if the Armijo line search or the Wolfe line sea...

Line search method and trust region method are two important classes of techniques for solving optimization problems and have their advantages respectively. In this paper we use the Armijo line search rule in a more accurate way and propose a new line search method for unconstrained optimization problems. Global convergence and convergence rate of the new method are analyzed under mild conditio...

Noise standard deviation (STD) is an important parameter in many digital image processing applications. This paper presents a Gaussian noise estimation algorithm using multiple singular value decomposition (SVD) and non-linear fitting. The proposed adds known to the original times generate noise-corrupted set then performs SVD on each image. By analyzing values of images, overdetermined equatio...

In the last decades, helicopter-borne electromagnetic (HEM) method became a focus of interest in the fields of mineral exploration, geological mapping, groundwater resource investigation and environmental monitoring. As a standard approach, researchers use 1-D inversion of the acquired HEM data to recover the conductivity/resistivity-depth models. Since the relation between HEM data and model ...

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...

This paper presents a benchmarking study on the steepest descent (SD) method considering three different line search conditions including Backtracking (BC), Armijo-Backtracking (ABC) and Goldstein (GC) in nonlinear least squares fitting of measured data obtained from coordinate measuring machine (CMM). Within this scope, five primitive geometries such as circle, square, rectangle, triangle elli...

We propose a variation of simplex-downhill algorithm specifically customized for optimizing parameters in statistical machine translation (SMT) decoder for better end-user automatic evaluation metric scores for translations, such as versions of BLEU, TER and mixtures of them. Traditional simplexdownhill has the advantage of derivative-free computations of objective functions, yet still gives sa...

In this paper, we develop a new nonmonotone Armijo-type line search for LS (Liu-Storey) conjugate gradient method for minimizing functions having Lipschitz continuous partial derivatives. The nonmonotone line search can guarantee the global convergence of original LS method under some mild conditions. AMS Subject Classification: 90C30, 65K05