Search results for "Approx"
showing 10 items of 922 documents
Hydrological post-processing based on approximate Bayesian computation (ABC)
2019
[EN] This study introduces a method to quantify the conditional predictive uncertainty in hydrological post-processing contexts when it is cumbersome to calculate the likelihood (intractable likelihood). Sometimes, it can be difficult to calculate the likelihood itself in hydrological modelling, specially working with complex models or with ungauged catchments. Therefore, we propose the ABC post-processor that exchanges the requirement of calculating the likelihood function by the use of some sufficient summary statistics and synthetic datasets. The aim is to show that the conditional predictive distribution is qualitatively similar produced by the exact predictive (MCMC post-processor) or …
Scheduling shared continuous resources on many-cores
2014
We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement rj∈[0,1]. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of r_j, it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their processing speeds, have been studied under the term discrete-continuous scheduling. Known results are either very pessimistic or heuristic in nature. In this paper, …
Numerical Approximation of Elliptic Variational Problems
2003
This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.
Indirect Methods for Optimal Control Problems
2003
This chapter is dedicated to the numerical approximation of Optimal Control Problems. The algorithms are based on the necessary conditions for optimality which allow us to use a descent method for the minimization of the cost functional.
New analytical approach to analyze the nonlinear regime of stochastic resonance
2015
We propose some approximate methods to explore the nonlinear regime of the stochastic resonance phenomenon. These approximations correspond to different truncation schemes of cumulants. We compare the theoretical results for the signal power amplification, obtained by using ordinary cumulant truncation schemes, that is Gaussian and excess approximations, the modified two-state approximation with those obtained by numerical simulations of the Langevin equation describing the dynamics of the system.
On smoothing problems with one additional equality condition
2009
Two problems of approximation in Hilbert spaces are considered with one additional equality condition: the smoothing problem with a weight and the smoothing problem with an obstacle. This condition is a generalization of the equality, which appears in the problem of approximation of a histogram in a natural way. We characterize the solutions of these smoothing problems and investigate the connection between them. First published online: 14 Oct 2010
Edge Orientation and the Design of Problem-Specific Crossover Operators for the OCST Problem
2012
In the Euclidean optimal communication spanning tree problem, the edges in optimal trees not only have small weights but also point with high probability toward the center of the graph. These characteristics of optimal solutions can be used for the design of problem-specific evolutionary algorithms (EAs). Recombination operators of direct encodings like edge-set and NetDir can be extended such that they prefer not only edges with small distance weights but also edges that point toward the center of the graph. Experimental results show higher performance and robustness in comparison to EAs using existing crossover strategies.
A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search
2017
The most fundamental problem encountered in the field of stochastic optimization, is the Stochastic Root Finding (SRF) problem where the task is to locate an unknown point x∗ for which g(x∗) = 0 for a given function g that can only be observed in the presence of noise [15]. The vast majority of the state-of-the-art solutions to the SRF problem involve the theory of stochastic approximation. The premise of the latter family of algorithms is to oper ate by means of so-called “small-step”processesthat explorethe search space in a conservative manner. Using this paradigm, the point investigated at any time instant is in the proximity of the point investigated at the previous time instant, render…
ε-Regularized two-level optimization problems: Approximation and existence results
2006
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
Uniformization of metric surfaces using isothermal coordinates
2021
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct suitable isothermal coordinates.