Dynamic programming approach to structural optimization problem – numerical algorithm

In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed

Les établissements publics territoriaux de bassin, pivots de l’action territoriale pour une gestion équilibrée de l’eau et des milieux aquatiques à l’échelle des bassins versants : Premiers retours d’expérience

Gérer l’eau, la terre et les ressources associées, c’est préparer le bien‑être économique et social et « écologique » sur le long terme. La réflexion sur la gestion de l’eau par les pouvoirs publics est donc une question essentielle.Une difficulté fait obstacle à une pratique en ce domaine : la géographie institutionnelle, celle de politiques publiques, et la géographie de l’eau, celle du territoire hydrographique, ne se recoupent pas.En 2003, le code de l’environnement reconnaissait les Établissements Publics Territoriaux de Bassin (EPTB), en tant qu’acteurs opérationnels de la gestion de l’eau.La spécificité des actions des ÉPTB se résume triplement par l’adaptation aux territoires, par leur capacité de planification et par leurs fonctions démocratiques.The good management of water and earth, with their associated resources, leads the way to effective economic, social and ecological well-being in the long term. It is essential, therefore, that the public authorities should give serious consideration to water management.One of the main difficulties in this field arises from the institutional geography: there is no immediate relationship between the geography of public policy and that of the water basin.In 2003, France’s individual water basin organizations, known as the EPTBs, were recognized as having operational responsibility for water management under the environmental code.The EPTBs’ specific actions can be summarized under three headings: adapting projects to meet the different needs of each territory; planning ability; and ensuring that “governance” (i.e. organisation and operation) is effected democratically

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

On-the-fly Approximation of Multivariate Total Variation Minimization

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Analysis of partnership and conservation requirements for a threatened species, Acipenser sturio L., 1758: Towards the implementation of a recovery plan

El esturión atlántico Acipenser sturio L., 1758 es una especie amenazada cuyo último santuario es el ecosistema Gironda, Garona y Dordoña. Se encuentra estrictamente protegido en Francia desde 1981. Sin embargo, no se ha producido un significativo incremento de esta población. Hasta recientemente, como con el programa desarrollado para el salmón, los planes de recuperación de las especies migratorias se han centrado principalmente en la adquisición de conocimiento y en el desarrollo de programas estrictamente técnicos. Estos enfoques son insuficientes para integrar los requerimientos de supervivencia de las especies en la gestión ambiental. El análisis de las necesidades requeridas para la recuperación del esturión atlántico sugiere aspectos técnicos fácilmente manejables, y las medidas apropiadas están disponibles. Por otro lado, aspectos sociales de recuperación más complejos pueden frecuentemente interferir con la puesta en práctica de acciones técnicas. Como un hecho natural, la gestión de los ecosistemas acuáticos trata con múltiples actores, con diferentes intereses y varias competencias, que pueden, directa o indirectamente, influir en la consecución del programa de recuperación. La motivación de todos los grupos de actores y su inclusión en un proyecto colectivo es una de las maneras de realizar los objetivos de un programa de recuperación.The Atlantic sturgeon Acipenser sturio L., 1758 is a threatened species whose last sanctuary is the Gironde, Garonne and Dordogne ecosystem. It has been strictly protected throughout France since 1981. However, no significant increase of its population has occurred. Until recently, as with the programme developed for salmon, migratory species restoration plans have mainly been centred on knowledge acquisition and the development of strictly technical programmes. These approaches are insufficient to integrate species survival requirements in environmental management. The analysis of needs necessary for the recovery of Atlantic sturgeon suggests easily manageable technical aspects, providing proper means are available. On the other hand, far more complex social aspects of recovery can often interfere with the implementation of technical actions. As a matter of fact, aquatic ecosystem management deals with multiple actors, with different concerns and various competencies, which can directly or indirectly influence the achievement of a restoration programme. Motivating each group of actors and including them in a collective project is one of the ways to achieve the goals of a restoration programme.Instituto Español de Oceanografí

A Parallel Inertial Proximal Optimization Method

International audienceThe Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of maximal operators. Based on this algorithm, parallel proximal algorithms are proposed to minimize over a linear subspace of a Hilbert space the sum of a finite number of proper, lower semicontinuous convex functions composed with linear operators. It is shown that particular cases of these methods are the simultaneous direction method of multipliers proposed by Stetzer et al., the parallel proximal algorithm developed by Combettes and Pesquet, and a parallelized version of an algorithm proposed by Attouch and Soueycatt