A derivative-free quasi-Newton-type algorithm in which its search direction is a product of positive definite diagonal matrix and residual vector presented. The simple to implement has the ability solve large-scale nonlinear systems equations with separable functions. simply obtained quasi-Newton manner at each iteration. Under some suitable conditions, global R-linear convergence result are Nu...

Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform based schemes result in eecient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an ima...

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit the piece-wise linear nature of the dual problem. The second part of the paper applies the previous result to acceleration of convex minimization problems, and...

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than...

The traditional quasi-Newton method for updating the approximate Hessian is based on the change in the gradient of the objective function. This paper describes a new update method that incorporates also the change in the value of the function. The method effectively uses a cubic approximation of the objective function to better approximate its directional second derivative. The cubic approximat...

Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization ...

While generalized equations with differentiable single-valued base mappings and the associated Josephy–Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush-Kuhn-Tucker optimality systems). We introduce for the general semismooth case appropriate notion...

In this article, we propose a new product positioning method based on the neural network methodology of a self-organizing map. The method incorporates the concept of rings of influence, where a firm evaluates individual consumers and decides on the intensity to pursue a consumer, based on the probability that this consumer will purchase a competing product. The method has several advantages ove...