Search results for "a priori"
showing 10 items of 136 documents
Comparison of different segmentation approaches without using gold standard. Application to the estimation of the left ventricle ejection fraction fr…
2011
International audience; A statistical method is proposed to compare several estimates of a relevant clinical parameter when no gold standard is available. The method is illustrated by considering the left ventricle ejection fraction derived from cardiac magnetic resonance images and computed using seven approaches with different degrees of automation. The proposed method did not use any a priori regarding with the reliability of each method and its degree of automation. The results showed that the most accurate estimates of the ejection fraction were obtained using manual segmentations, followed by the semiautomatic methods, while the methods with the least user input yielded the least accu…
Convergence in car prices among European countries
2011
This article contributes to the literature on price convergence in Europe by investigating the existence of stochastic and deterministic convergence of car prices in the EU15 countries. We apply recently developed econometric techniques that allow for multiple structural breaks to an up-to-date dataset. We find considerable evidence of both types of convergence in our sample of countries and car models, therefore suggesting a tendency for relative prices to equalize over time. In addition, we find evidence regarding the importance in this convergence process of both legislative changes taking place in the years 1996 and 2002, and the implementation of Economic and Monetary Union (EMU).
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants
2004
In the present paper, we analyze computational properties of the functional type a posteriori error estimates that have been derived for elliptic type boundary-value problems by duality theory in calculus of variations. We are concerned with the ability of this type of a posteriori estimates to provide accurate upper bounds of global errors and properly indicate the distribution of local ones. These questions were analyzed on a series of boundary-value problems for linear elliptic operators of 2nd and 4th order. The theoretical results are confirmed by numerical tests in which the duality error majorant for the classical diffusion problem is compared with the standard error indicator used i…
Multi-scenario multi-objective robust optimization under deep uncertainty: A posteriori approach
2021
This paper proposes a novel optimization approach for multi-scenario multi-objective robust decision making, as well as an alternative way for scenario discovery and identifying vulnerable scenarios even before any solution generation. To demonstrate and test the novel approach, we use the classic shallow lake problem. We compare the results obtained with the novel approach to those obtained with previously used approaches. We show that the novel approach guarantees the feasibility and robust efficiency of the produced solutions under all selected scenarios, while decreasing computation cost, addresses the scenario-dependency issues, and enables the decision-makers to explore the trade-off …
Two-Sided Guaranteed Estimates of the Cost Functional for Optimal Control Problems with Elliptic State Equations
2014
In the paper, we discuss error estimation methods for optimal control problems with distributed control functions entering the right-hand side of the corresponding elliptic state equations. Our analysis is based on a posteriori error estimates of the functional type, which were derived in the last decade for many boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation. If they are applied to approximate solutions of state equations, then we obtain new variational formulations of optimal control problems and guaranteed bounds of the cost functional. Moreover, for problems with linear state equations this procedure leads to gu…
An Island Strategy for Memetic Discrete Tomography Reconstruction
2014
In this paper we present a parallel island model memetic algorithm for binary discrete tomography reconstruction that uses only four projections without any further a priori information. The underlying combination strategy consists in separated populations of agents that evolve by means of different processes. Agents progress towards a possible solution by using genetic operators, switch and a particular compactness operator. A guided migration scheme is applied to select suitable migrants by considering both their own and their sub-population fitness. That is, from time to time, we allow some individuals to transfer to different subpopulations. The benefits of this paradigm were tested in …
A Priori Methods
1998
In the case of a priori methods, the decision maker must specify her or his preferences, hopes and opinions before the solution process. The difficulty is that the decision maker does not necessarily know beforehand what it is possible to attain in the problem and how realistic her or his expectations are. The working order in these methods is: 1) decision maker, 2) analyst.
Reference point based multi-objective evolutionary algorithms for group decisions
2008
While in the past decades research on multi-objective evolutionary algorithms (MOEA) has aimed at finding the whole set of Pareto optimal solutions, current approaches focus on only those parts of the Pareto front which satisfy the preferences of the decision maker (DM). Therefore, they integrate the DM early on in the optimization process instead of leaving him/her alone with the final choice of one solution among the whole Pareto optimal set. In this paper, we address an aspect which has been neglected so far in the research on integrating preferences: in most real-world problems, there is not only one DM, but a group of DMs trying to find one consensus decision all participants are wille…