A technique for maintaining the positive definiteness of the matrices in the quasi-Newton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a so-called piecewise line-search technique, while their positive...

This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newt...

Diamondoids are cage-like saturated hydrocarbons consisting of fused cyclohexane rings. The Diamondoids family of compounds is one of the best candidates for molecular building blocks (MBBs) in nanotechnology to construct organic nanostructures compared to other MBBs known so far. The challenge is to find a route for self-assembly of these cage hydrocarbons and their applications in the bottom-...

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after m steps) for solving nonlinear equations, F(x) = 0, F : D ⊆ Rn → Rn. We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given n, there exist thresholds of m, that is an interval (...

An efficient black-box algorithm for self-consistent analysis of three-dimensional (3-D) microelectromechanical systems (MEMS) is described. The algorithm is matrix-free based and employs a multilevel Newton technique to solve the coupled electromechanical equations. The new approach is shown to converge very rapidly and is much faster than relaxation algorithm for tightly coupled cases. While ...

In this paper, we first give a new equivalent optimization form to nonlinear complementarity problems and then establish a damped Newton method in which penalty technique is used. The subproblems of the method are lower-dimensional linear complementarity problems. We prove that the algorithm converges globally for strongly monotone complementarity problems. Under certain conditions, the method ...

This paper presents a Newton-iteration method for obtaining a J-J spectral factorisation of systems from non-parametric characterisations using identification techniques. Systems are assumed to be Fréchet differentiable discrete-time maps. The technique may be used on nonlinear nonparametric time-response representations. The scheme requires stabilised identification and stabilised inverse iden...

In this paper a new parallel algorithm for the computation of the inverse of a bivariate polynomial matrix are presented. The parallel algorithm based on the technique evaluation-interpolation and for the part of interpolation uses the Newton bivariate polynomial interpolation. The algorithm is applied to the programming environment of MATLAB with Parallel Computing Toolbox and is compared to t...

Huber’s M-estimation technique is applied to a block-angular regression problem, which may arise from some applications. A recursive, modified Newton approach to computing the estimates is presented. The structure of the problem is exploited to make the algorithm efficient. It is shown how to efficiently compute a descent search direction by using updating/downdating techniques for matrix facto...