Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable met...

WSNs are important to enemies and they get to be powerless to a few sorts of assaults since they are sent in open and unprotected situations. Because of the constrained assets of WSNs, it is trying to consolidate essential security components, for example, verification, key conveyance and protection in WSNs. In any case, trust administration that models the trust on the conduct of components of...

We extend the theory of Sobolev gradients to include variable metric methods, such as Newton’s method and the Levenberg-Marquardt method, as gradient descent iterations associated with stepwise variable inner products. In particular, we obtain existence, uniqueness, and asymptotic convergence results for a gradient flow based on a variable inner product.

Given a function f0 defined on the unit square Ω with values in R, we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f0 on the boundary nodes, and the image of f has minimal surface area. The problem is formulated as that of minimizing a discretization of a least squares functional whose critical points are uniformly parameterized minimal surfaces. The n...

In some recent papers, a method was developed of reducing coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable. In this paper, we apply the mentioned method and obtain some coupled fixed point results for mappings satisfying φ-weak contractive conditions in ordered b-metric spaces. Examples show how these...

For the problem of solving maximal monotone inclusions, we present a rather general class of algorithms, which contains hybrid inexact proximal point methods as a special case and allows for the use of a variable metric in subproblems. The global convergence and local linear rate of convergence are established under standard assumptions. We demonstrate the advantage of variable metric implement...

fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. several methods for evaluating fuzzy coefficients in linear regression models have been proposed. the first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. in this the...

We introduce a method for deriving a metric, locally based on the Fisher information matrix, into the data space. A self-organizing map (SOM) is computed in the new metric to explore financial statements of enterprises. The metric measures local distances in terms of changes in the distribution of an auxiliary random variable that reflects what is important in the data. In this paper the variab...