M. A. Katsoulakis, G. Kossioris and Ch. Makridakis Abstract. We study discrete and semidiscrete relaxation schemes for multidimensional scalar conservation laws. We show convergence of the relaxation schemes to the entropy solution of the conservation law and derive error estimates that exhibit the precise interaction between the relaxation time and the space/time discretization parameters of t...

One strategy for proving the global existence of admissible solutions to the Cauchy problem for first-order systems of conservation laws, is to introduce a small amount of diffusion and then pass to the limit. Under some structural assumption, this task was achived by DiPerna when the diffusion is given by artificial viscosity. We showed recently that this program works also for the Jin–Xin rel...

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag –Leffler function and the Fox function. The conditions of a change from the Debye relaxation to “slow” (anomalous) relaxation with a power time dependence have been examined ...

We show that a simple relaxation scheme of the type proposed by Jin and Xin Comm. Pure Appl. Math. 48(1995) pp. 235{276] can be reinterpreted as deening a particular approximate Riemann solver for the original system of m conservation laws. Based on this observation, a more general class of approximate Riemann solvers is proposed which allows as many as 2m waves in the resulting solution. These...

We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the s...

Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula...

formalized in terms of a hypergraph G = (V,E) whose edges arrive one-by-one and the goal is to construct an edge cover F ⊆ E with the objective of minimizing the cardinality (or cost in the weighted case) of F . We further consider a parameterized relaxation of this problem, where given some 0 ≤ < 1, the goal is to construct an edge (1− )-cover, namely, a subset of edges incident to all but an ...

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficult, and therefore approximate inference methods based on a linear programming ...

There are many (mixed) integer programming formulations of the Steiner problem in networks. The corresponding linear programming relaxations are of great interest particularly, but not exclusively, for computing lower bounds; but not much has been known about the relative quality of these relaxations. We compare all classical and some new relaxations from a theoretical point of view with respec...

We investigate a model for buffer management of multi-class traffic into a finite shared buffer. A hierarchy of increasingly stronger linear programming relaxations for this model is proposed. The number of hierarchies equals the number of job classes. Each relaxation in the hierarchy is constructed by projecting the original achievable performance region into a polytope with fewer variables an...