Search results for "convex"
showing 10 items of 389 documents
Geodesic flow of the averaged controlled Kepler equation
2008
A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…
Convergence rate of a relaxed inertial proximal algorithm for convex minimization
2018
International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.
Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits
2015
International audience; The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature computations, geodesic convexity), the time minimal case is associated to a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers. In particular we prove geodesic convexity of the elliptic domain.
Covariations between shell-growth parameters and the control of the ranges of variation of functionally relevant shell-shape parameters in bivalves: …
2014
Major traits of shell shape in bivalves may alternatively be described in terms of (i) functionally relevant parameters, assumed to play a significant role in the adaptation of bivalves molluscs to their environments (such as the shell-outline elongation E, ventral convexity K, and dissymmetry D), or (ii) growth-based parameters, directly controlled by the animal. Due to the geometrical linkage between functionally-relevant and growth-based parameters, adaptive constraints that may either widen or narrow the respective ranges of variations of the functional parameters lead to the onset of specific covariations (either positive or negative) between the growth-based parameters. This has pract…
Covarying shell growth parameters and the regulation of shell shape in marine bivalves: a case study on Tellinoidea.
2014
Specific parameters characterising shell shape may arguably have a significant role in the adaptation of bivalve molluscs to their particular environments. Yet, suchfunctionally relevantshape parameters (shell outline elongation, dissymmetry, and ventral convexity) are not those parameters that the animal may directly control. Rather than shell shape, the animal regulates shell growth. Accordingly, an alternative,growth-baseddescription of shell-shape is best fitted to understand how the animal may control the achieved shell shape. The key point is, in practice, to bring out the link between those two alternative modes of shell-shape descriptions, that is, to derive the set of equations whi…
Joint Optimization of Sensor Selection and Routing for Distributed Estimation in Wireless Sensor Networks
2014
Avances recientes en redes inalámbricos de sensores (WSNs, Wireless Sensor Networks) han posibilitado que pequeños sensores, baratos y con recursos limitados tanto en sensado, comunicación, como en computación, sean desplegados a gran escala. En consecuencia, las WSNs pueden ofrecer diversos servicios en importantes aplicaciones para la sociedad. Entre las varias restricciones que aparecen en el diseño de WSNs, tales como la limitación en energía disponible, procesamiento y memoria, la limitación en energía es muy importante ya que en muchas aplicaciones (ej., monitorización remota de diferentes entornos, edificios administrativos, monitoreo del hábitat, los incendios forestales, la atenció…
Overland flow generation on hillslopes of complex topography: analytical Solutions
2007
The analytical solution of the overland flow equations developed by Agnese et al. (2001; Hydrological Processes15: 3225–3238) for rectangular straight hillslopes was extended to convergent and divergent surfaces and to concave and convex profiles. Towards this aim, the conical convergent and divergent surfaces are approximated by a trapezoidal shape, and the overland flow is assumed to be always one-dimensional. A simple ‘shape factor’ accounting for both planform geometry and profile shape was introduced: for each planform geometry, a brachistochrone profile was obtained by minimizing a functional containing a slope function of the profile. Minima shape factors are associated with brachist…
Convex analysis and dual problems
2018
Tässä tutkielmassa tarkastellaan valittujen variaatiolaskennan ongelmien ja näiden duaaliongelmien välisiä suhteita. Tutkielmassa esitetään aiheen yleinen teoria ja annetaan esimerkkejä sovelluksista.
Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces
2020
In this study, some Baum-Katz’s type theorems for pairwise independent random elements are extended to a metric space endowed with a convex combination operation. Our results are considered in the cases of identically distributed and non-identically distributed random elements. Some illustrative examples are provided to sharpen the results. peerReviewed
Lower bound limit analysis by bem: Convex optimization problem and incremental approach
2013
Abstract The lower bound limit approach of the classical plasticity theory is rephrased using the Multidomain Symmetric Galerkin Boundary Element Method, under conditions of plane and initial strains, ideal plasticity and associated flow rule. The new formulation couples a multidomain procedure with nonlinear programming techniques and defines the self-equilibrium stress field by an equation involving all the substructures (bem-elements) of the discretized system. The analysis is performed in a canonical form as a convex optimization problem with quadratic constraints, in terms of discrete variables, and implemented using the Karnak.sGbem code coupled with the optimization toolbox by MatLab…