In this paper we propose a purely distributed dynamic network routing algorithm that simultaneously regulates queue sizes across the network. The algorithm is distributed since each node decides on its outgoing link flows based only on its own and its immediate neighbors’ information. Therefore, this routing method will be adaptive and robust to changes in the network topology, such as the node...

Under special conditions an approximate wave front solution to a system of nonlinear reaction-diffusion type equations is obtained. An assumption of fast kinetics permits the system to be reformulated as a single nonlinear differential-integral equation of convolution type. If the convolution kernel has the form of a mollifier then the convolution is localized to obtain an infinite system of di...

Abstract. We deduce the kinetic equations describing the low density (and the large number of particles) limit of interacting particle systems with k-nary interaction of pure jump type supplemented by an underlying ”free motion” being an arbitrary Feller process. The well posedness of the Cauchy problem together with the propagation of chaos property are proved for these kinetic equations under...

We introduce and analyze a stable procedure for the approximation of 〈f†, φ〉 where f† is the least residual norm solution of the minimal norm of the ill-posed equation Af = g, with compact operator A : X → Y between Hilbert spaces, and φ ∈ X has some smoothness assumption. Our method is based on a finite number of singular values of A and some finite rank operators. Our results are in a more ge...

In this paper, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg Lfunctions. One of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average. A first consequence is a new subconvexity bound for Rankin-Selberg L-functions...

We introduce a novel subgradient optimization-based framework for iterative peak-to-average power ratio (PAR) reduction for multicarrier systems, such as wireless orthogonal frequency division multiplexing (OFDM) and wireline discrete multitone (DMT) very high-speed digital subscriber line (DMT-VDSL) systems. The proposed approach uses reserved or unused tones to minimize the peak magnitude of ...

We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradien...

Time series averaging in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems. This article proposes and analyzes subgradient methods for the problem of finding a sample mean in DTW spaces. The class of subgradient methods generalizes existing sample mean algorithms such as DTW Barycenter Averaging (DBA). We show that DBA is a majorize-minimize ...

In this lecture, we discuss first order methods for the minimization of convex functions. We focus almost exclusively on subgradient-based methods, which are essentially universally applicable for convex optimization problems, because they rely very little on the structure of the problem being solved. This leads to effective but slow algorithms in classical optimization problems, however, in la...

In this paper we address the problem of multi-agent optimization for convex functions expressible as sums of convex functions. Each agent has access to only one function in the sum and can use only local information to update its current estimate of the optimal solution. We consider two consensus-based iterative algorithms, based on a combination between a consensus step and a subgradient decen...