Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Schiela, Anton"'
The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined on arbitrary sets that do not necessarily bear any structure at all. Th
Externí odkaz:
http://arxiv.org/abs/2409.04492
Autor:
Weigl, Laura, Schiela, Anton
We consider Newton's method for finding zeros of mappings from a manifold $\mathcal{X}$ into a vector bundle $\mathcal{E}$. In this setting a connection on $\mathcal{E}$ is required to render the Newton equation well defined, and a retraction on $\ma
Externí odkaz:
http://arxiv.org/abs/2404.04073
Extended dynamic mode decomposition (EDMD) is a well-established method to generate a data-driven approximation of the Koopman operator for analysis and prediction of nonlinear dynamical systems. Recently, kernel EDMD (kEDMD) has gained popularity du
Externí odkaz:
http://arxiv.org/abs/2403.18809
This paper proposes a novel approach to adaptive step sizes in stochastic gradient descent (SGD) by utilizing quantities that we have identified as numerically traceable -- the Lipschitz constant for gradients and a concept of the local variance in s
Externí odkaz:
http://arxiv.org/abs/2311.16956
We consider Proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global convergence a
Externí odkaz:
http://arxiv.org/abs/2204.12168
Publikováno v:
J.Optim.Theory.Appl. 195 (2022) 596-623
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the fea
Externí odkaz:
http://arxiv.org/abs/2110.04882
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering differentiability and
Externí odkaz:
http://arxiv.org/abs/2103.14344
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gra
Externí odkaz:
http://arxiv.org/abs/2012.01848
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs
We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end, we present
Externí odkaz:
http://arxiv.org/abs/2008.13001
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which
Externí odkaz:
http://arxiv.org/abs/2007.14446