We propose a strategy for building up the linear program while using a logarithmic barrier method. The method starts with a (small) subset of the dual constraints, and follows the corresponding central path until the iterate is close to (or violates) one of the constraints, which is in turn added to the current system. This process is repeated until an optimal solution is reached. If a constrai...

We describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. We present a new method for computing, electronic transport wave function and Greens function of the disordered Graphene. In this method, based on the small rectangular approximation, break up the potential barriers in to small parts. Then using the f...

Abstract: An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton m...

A classic method to compute the mass function of dark matter halos is the excursion set method, where the density perturbation evolves stochastically with the smoothing scale, and the problem of computing the probability of halo formation is mapped into the so-called first-passage time problem in the presence of a barrier. To date, however, analytical results were only obtained if the density p...

This paper presents a safety-aware learning framework that employs an adaptive model learning method together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique, and the resulting model will be used in combination with control barrier certificates which constrain feedback control...

This paper is the second of a series of three where we study the mass function of virialized dark matter halos using the excursion set method. Motivated by recent large-scale N-body simulations determining the relation between the density threshold for gravitational collapse and the variance of the linear density field for regions that collapse to form halos by the present epoch, we deduce that...

We generalize results about the classical Schottky groups to quasiconvex subgroups in negatively curved groups, answering a question of M. Bestvina.