We propose an energy-efficient procedure for transponder configuration in FMF-based elastic optical networks in which quality of service and physical constraints are guaranteed and joint optimization of transmit optical power, temporal, spatial and spectral variables are addressed. We use geometric convexification techniques to provide convex representations for quality of service, transponder ...

Abstract: Engineering optimization problems are normally formulated as nonlinear programming problems and adopted in a lot of research to show the effectiveness of new optimization algorithms. These problems are usually solved through deterministic or heuristic methods. Because non-convex functions exist in most engineering optimization problems that possess multiple local optima, the heuristic...

We consider a Mayer problem of optimal control, whose dynamic constraint is given by a convex-valued differential inclusion. Both state and endpoint constraints are involved. We prove necessary conditions incorporating the Hamiltonian inclusion, the Euler-Lagrange inclusion, and the WeierstrassPontryagin maximum condition. Our results weaken the hypotheses and strengthen the conclusions of earl...

The goal of this paper is threefold. It first describes a novel way of measuring disagreement between rankings of a finite set X of n ≥ 1 elements, that can be viewed as a (mass transportation) Kantorovich metric, once the collection rankings of X is embedded in the set Kn of n× n doubly-stochastic matrices. It also shows that such an embedding makes it possible to define a natural notion of me...

The Cauchy-Born rule postulates that when a monatomic crystal is subjected to a small linear displacement of its boundary, then all atoms will follow this displacement. In the absence of previous mathematical results, we study the validity of this rule in the model case of a 2D cubic lattice interacting via harmonic springs between nearest and diagonal neighbours. Our main result is that for fa...

This article introduces a generalization of discrete Optimal Transport that includes a regularity penalty and a relaxation of the bijectivity constraint. The corresponding transport plan is solved by minimizing an energy which is a convexification of an integer optimization problem. We propose to use a proximal splitting scheme to perform the minimization on large scale imaging problems. For un...

We propose a new hardware ray casting algorithm for unstructured meshes composed of tetrahedral cells. Our work builds on the technique published at IEEE Visualization 2003 by Weiler et al.. Our contributions can be divided into three categories. First, we propose an alternate representation for mesh data in 2D textures that is more compact and efficient, compared to the 3D textures used in the...

Let (QP ) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear constraints. In this paper, we present a general method to solve (QP ) by reformulation of the problem into an equivalent 0-1 program with a convex quadratic objective function, followed by the use of a standard mixed integer quadratic programming solver. Our convexification method, which is...

This work investigates the computational procedures used to obtain global solution to the Economic Linear Optimal Control (ELOC) problem. The proposed method employs the Generalized Benders Decomposition (GBD) algorithm. Compared to the previous branch and bound approach, a naive application GBD to the ELOC problem will improve computational performance, due to less frequent calls to computatio...

We consider in this paper the homogeneous 1-D wave equation defined on Ω ⊂ R. Using the Hilbert Uniqueness Method, one may define, for each subset ω ⊂ Ω, the exact control vω of minimal L (ω × (0, T ))-norm which drives to rest the system at a large enough time T > 0. We address the question of the optimal position of ω which minimizes the functional J : ω → ||vω||L2(ω×(0,T )). We express the s...