Searched for: subject%3A%22saddle%255C%2Bpoint%22
(1 - 20 of 28)

Pages

document
Vakili, Seryas (author), Ebadi, G. (author), Vuik, Cornelis (author)
In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of...
journal article 2022
document
Qiu, Yue (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, Cornelis (author)
In this article, we study preconditioning techniques for the control of the Navier–Stokes equation, where the control only acts on a few parts of the domain. Optimization, discretization, and linearization of the control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system...
journal article 2021
document
Groeneboom, P. (author)
Let (Formula presented.) be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left-continuous slope of the least concave majorant of the empirical distribution function. For a sample from the uniform distribution, the asymptotic distribution of the L<sub>2</sub>-distance of the...
journal article 2020
document
Rahrah, M. (author), Lopez Pena, L.A. (author), Vermolen, F.J. (author), Meulenbroek, B.J. (author)
Water injection in the aquifer induces deformations in the soil. These mechanical deformations give rise to a change in porosity and permeability, which results in non-linearity of the mathematical problem. Assuming that the deformations are very small, the model provided by Biot’s theory of linear poroelasticity is used to determine the...
journal article 2020
document
Verwer, S.E. (author), Nadeem, A. (author), Hammerschmidt, C.A. (author), Bliek, L. (author), Al-Dujaili, Abdullah (author), O’Reilly, Una-May (author)
Training classifiers that are robust against adversarially modified examples is becoming increasingly important in practice. In the field of malware detection, adversaries modify malicious binary files to seem benign while preserving their malicious behavior. We report on the results of a recently held robust malware detection challenge. There...
conference paper 2020
document
Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, C. (author)
In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle...
report 2015
document
Qiu, Y. (author)
Optimal flow control problems are important for applications in science and engineering. Solving such problems usually requires the solution of a large linear generalized saddle-point system. This linear system is sparse and highly indefinite. In order to solve such systems using Krylov subspace methods, efficient preconditioners are necessary...
doctoral thesis 2015
document
Hou, Z. (author), Bociort, F. (author)
A major challenge in lens design is the presence of many local minima in the optimization landscape. However, unlike other global optimization problems, the lens design landscape has an additional structure, that can facilitate the design process: many local minima are closely related to minima of simpler problems. For discussing this property,...
conference paper 2015
document
Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)
In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle...
report 2015
document
Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)
In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point...
report 2014
document
Bociort, F. (author), van Grol, P. (author)
Understanding the structure of the design space in optical system optimization is difficult, because common human intuition fails when it encounters the challenge of high dimensionality, resulting from the many optimization parameters of lens systems. However, a deep mathematical idea, that critical points structure the properties of the space...
conference paper 2012
document
Bociort, F. (author)
The presence of many local minima in the merit function landscape is perhaps the most difficult challenge in lens design. We present a simplified mathematical model that illustrates why the number of local minima increases rapidly with each additional lens added to the imaging system. Comparisons with results obtained with lens design software...
conference paper 2010
document
Bociort, F. (author), Van Grol, P. (author)
In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where...
conference paper 2010
document
Bociort, F. (author), Van Grol, P. (author)
In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where...
conference paper 2010
document
Van Grol, P. (author), Bociort, F. (author), Van Turnhout, M. (author)
Contrary to the frequent tacit assumption that the local minima of a merit function are points scattered more or less randomly over the design landscape, we have found that, at least for simple imaging systems (doublets with three and triplets with five variables) all design shapes we have observed thus far form a strictly ordered set of points,...
conference paper 2009
document
Bociort, F. (author), Van Turnhout, M. (author)
journal article 2009
document
Van Turnhout, M. (author)
A major problem in optical system design is that the optical merit function landscape is usually very complicated, especially for complex design problems where many minima are present. Finding good new local minima is then a difficult task. We show however that a certain degree of order is present in the optical design space, which is best...
doctoral thesis 2009
document
Marinescu, O. (author), Bociort, F. (author)
journal article 2008
document
Marinescu, O. (author), Bociort, F. (author)
journal article 2008
document
Bociort, F. (author), Van Turnhout, M. (author), Marinescu, O. (author)
Saddle-point construction (SPC) is a new method to insert lenses into an existing design. With SPC, by inserting and extracting lenses new system shapes can be obtained very rapidly, and we believe that, if added to the optical designer’s arsenal, this new tool can significantly increase design productivity in certain situations. Despite the...
conference paper 2007
Searched for: subject%3A%22saddle%255C%2Bpoint%22
(1 - 20 of 28)

Pages