On a linear differential equation of the advanced type

A linear differential equation of the advanced type is considered. Existence of solutions for any finite interval is shown. Also, a method for generating all the solutions is described and justified

Nonparametric Modeling and Model-Based Control of the Insulin-Glucose System

Non

A cone programming approach to the bilinear matrix inequality problem and its geometry

We discuss an approach for solving the Bilinear Matrix Inequality (BMI) based on its connections with certain problems defined over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, we show that solving a given BMI is equivalent to examining the solution set of a suitably constructed Cone-LP or Cone-LCP. This approach facilitates our understanding of the geometry of the BMI and opens up new avenues for the development of the computational procedures for its solution.

On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation

. We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. The values of each function are assumed to reside at a different memory element. A single processing element is designated to approximate the value of the maximum of the sum of these functions by adopting a certain protocol. Under certain assumptions on the class of permissible protocols, we obtain the minimumnumber of real valued messages that has to be transferred between the processing element and the memory elements in order to find the desired approximation of this maximum. In particular, we exploit the optimality of the non-adaptive protocols for the Lipschitzian optimization problem, studied in the context of information-based complexity, to prove our main result. Keywords: Lipschitzian Optimization; Communication Complexity; Coordinated Model of Computation i Glossary of Symbols ! the set of real numbers := defined as jj:jj the infinity norm [0; 1] p the p-dimensional ..