This conference paper provides an overview of the material presented in two field electron emission tutorial lectures given at the 2016 Young Researchers' School in Vacuum Microand NanoElectronics, held in Saint-Petersburg in October 2016. This paper aims to indicate the scope and structure of the tutorials, and also where some of the related published material can be found. Keywords—field elec...

We provide a simple interpretation of the use of the logarithmic barrier function in convex and linear programming. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 90C05; 90C25

Similar with the CLF method, Wieland and Allgöwer in [8] have proposed the construction of Control Barrier Functions (CBF), where the Lyapunov function is interchanged with the Barrier certificate studied in [3]. Using a CBF as in [8], one can design a universal feedback law for steering the states from the set of initial conditions to the set of terminal conditions, without violating the set o...

In this paper we propose a large{step analytic center method for smooth convex programming. The method is a natural implementation of the classical method of centers. It is assumed that the objective and constraint functions ful l the socalled Relative Lipschitz Condition, with Lipschitz constant M > 0. A great advantage of the method, above the existing path{following methods, is that the step...

Recently, reformulation of variational inequalities and complementarity problems as a system of equations or an optimization problem has become a hot topic in the eld of mathematical programming. Various merit functions play important roles in such reformulations. In this paper, among others, we consider the well-known Fischer function and explore its relationship with other merit functions. It...

We consider the Riemannian geometry defined on a convex set by the Hessian of a selfconcordant barrier function, and its associated geodesic curves. These provide guidance for the construction of efficient interior-point methods for optimizing a linear function over the intersection of the set with an affine manifold. We show that algorithms that follow the primal-dual central path are in some ...