In this work we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These problems consist of minimizing a nonlinear differentiable objective function subject to some nonlinear second-order cone constraints. Given a point interior to the feasible set defined by the nonlinear constraints, the proposed approach computes a feasible and descent direct...

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(2), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transfo...

A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-Epreinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic proper...

in this study, a multi-objective genetic algorithm (moga) is utilized to extract interpretable and compact fuzzy rule bases for modeling nonlinear multi-input multi-output (mimo) systems. in the process of non- linear system identi cation, structure selection, parameter estimation, model performance and model validation are important objectives. furthermore, se- curing low-level and high-level ...

We generalize substructuring methods to problems for functions f : Ω → M , where Ω is a domain in R and M is a Riemannian manifold. Examples for such functions include configurations of liquid crystals, ferromagnets, and deformations of Cosserat materials. We show that a substructuring theory can be developed for such problems. While the theory looks very similar to the linear theory on a forma...

This article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations (ODEs). I propose modeling lack of fit as a time-varying correction to the right-hand side of a proposed differential equation. This correction can be described as being a set of additive forcing functions, estimated from data. Representing lack of fit in this manner all...

Abstract. In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the co...

The brain can be regarded as an ensemble of connected dynamical systems and as such conforms to some simple principles relating the inputs and outputs of its constituent parts. The ensuing implications, for the way we think about, and measure, neuronal interactions, can be quite profound. These range from 1) implications for which aspects of neuronal activity are important to measure and how to...

The application of the genetic algorithm to the approximation of nonlinear transfer functions is considered. It is shown that the GA approximation method gives better accuracy than the classical Chebyshev approximation, which is sometimes considered to be the best available method for the minimax criterion. Other advantages of the proposed method include the ability to carry out a global search...