In this paper, we investigate the use of two-term piecewise quadratic Lyapunov functions for robust stability of linear time-varying systems. By using the so-called S-procedure and a special variable reduction method, we provide numerically e cient conditions for the robust asymptotic stability of the linear time-varying systems involving the convex combinations of two matrices. An example is i...

We prove that for every two convex polytopes P, Q ∈ R with vol(P ) = vol(Q), there exists a continuous piecewise-linear (PL) volume-preserving map f : P → Q. The result extends to general PL-manifolds. The proof is inexplicit and uses the corresponding fact in the smooth category, proved by Moser in [Mo]. We conclude with various examples and combinatorial applications.

in this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.when the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. additionally for linear feasibil...

2 Toric Varieties 7 2.1 Constructing an atlas for a toric variety from a fan . . . . . . . . . . . . . . . . . . . . 7 2.2 Cones correspond to torus orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Maps of fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

This short paper gives an introduction to the \emph{rcss} package. The R package \emph{rcss} provides users with a tool to approximate the value functions in the Bellman recursion using convex piecewise linear functions formed using operations on tangents. A pathwise method is then used to gauge the quality of the numerical results.

The recently developed technique for computation of piecewise quadratic Lyapunov functions is specialized to Lyapunov functions that are piecewise linear. This establishes a unified framework for computation of quadratic, piecewise quadratic, piecewise linear and polytopic Lyapunov functions. The search for a piecewise linear Lyapunov function is formulated as a linear programming problem, and ...

This paper studies a routing problem in a multimodal network with shipment consolidation options. A freight forwarder can use a mix of flexible-time and scheduled transportation services. Time windows are a prominent aspect of the problem. For instance, they are used to model opening hours of the terminals, as well as pickup and delivery time slots. The various features of the problem can be de...

Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm. Mots clés : Arbres couvrants de poids minimum, sécurisation des réseaux.