The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
Christian Ebenbauer - One of the best experts on this subject based on the ideXlab platform.
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a Smooth Vector Field for quadratic programming
Conference on Decision and Control, 2012Co-Authors: Hansbernd Durr, Erkin Saka, Christian EbenbauerAbstract:In this paper we consider the class of convex optimization problems with affine inequality constraints and focus hereby on the class of quadratic programs. We propose a Smooth Vector Field that is constructed such that its trajectories converge to the saddle point of the Lagrangian function associated to the convex optimization problem. We establish global asymptotic stability as well as exponential stability under mild assumptions for different variants of the Vector Field and propose a continuous-time Nesterov method.
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a Smooth Vector Field for saddle point problems
Conference on Decision and Control, 2011Co-Authors: Hansbernd Durr, Christian EbenbauerAbstract:In this paper we propose a novel Smooth Vector Field whose trajectories globally converge to the saddle point of the Lagrangian associated with a convex and constrained optimization problem. Under suitable assumptions, we prove global convergence of the trajectories for the class of strictly convex problems and we propose a Vector Field for linear programs.
Michel Laurent - One of the best experts on this subject based on the ideXlab platform.
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Sharp spectral asymptotics for non-reversible metastable diffusion processes
2020Co-Authors: Le Peutrec Dorian, Michel LaurentAbstract:Let $U_h:\mathbb R^{d}\to \mathbb R^{d}$ be a Smooth Vector Field and consider the associated overdamped Langevin equation $$dX_t=-U_h(X_t)\,dt+\sqrt{2h}\,dB_t$$ in the low temperature regime $h\rightarrow 0$. In this work, we study the spectrum of the associated diffusion $L=-h\Delta+U_h\cdot\nabla$ under the assumptions that $U_h=U_{0}+h\nu$, where the Vector Fields $U_{0}:\mathbb R^{d}\to \mathbb R^{d}$ and $\nu:\mathbb R^{d}\to \mathbb R^{d}$ are independent of $h\in(0,1]$, and that the dynamics admits $e^{-\frac Vh}$ as an invariant measure for some Smooth function $V:\mathbb{R}^d\rightarrow\mathbb{R}$. Assuming additionally that $V$ is a Morse function admitting $n_0$ local minima, we prove that there exists $\epsilon>0$ such that in the limit $h\to 0$, $L$ admits exactly $n_0$ eigenvalues in the strip $\{\operatorname{Re}(z)< \epsilon\}$ which have moreover exponentially small moduli. Under a generic assumption on the potential barriers of the Morse function $V$, we also prove that the asymptotic behaviors of these small eigenvalues are given by Eyring-Kramers type formulas
Laurent Michel - One of the best experts on this subject based on the ideXlab platform.
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Sharp spectral asymptotics for non-reversible metastable diffusion processes
2020Co-Authors: Dorian Le Peutrec, Laurent MichelAbstract:Let $U_h:\mathbb R^{d}\to \mathbb R^{d}$ be a Smooth Vector Field and consider the associated overdamped Langevin equation $$dX_t=-U_h(X_t)\,dt+\sqrt{2h}\,dB_t$$ in the low temperature regime $h\rightarrow 0$. In this work, we study the spectrum of the associated diffusion $L=-h\Delta+U_h\cdot\nabla$ under the assumptions that $U_h=U_{0}+h\nu$, where the Vector Fields $U_{0}:\mathbb R^{d}\to \mathbb R^{d}$ and $\nu:\mathbb R^{d}\to \mathbb R^{d}$ are independent of $h\in(0,1]$, and that the dynamics admits $e^{-\frac Vh}$ as an invariant measure for some Smooth function $V:\mathbb{R}^d\rightarrow\mathbb{R}$. Assuming additionally that $V$ is a Morse function admitting $n_0$ local minima, we prove that there exists $\epsilon>0$ such that in the limit $h\to 0$, $L$ admits exactly $n_0$ eigenvalues in the strip $\{0\leq \operatorname{Re}(z)< \epsilon\}$, which have moreover exponentially small moduli. Under a generic assumption on the potential barriers of the Morse function $V$, we also prove that the asymptotic behaviors of these small eigenvalues are given by Eyring-Kramers type formulas.
Tere Mseara - One of the best experts on this subject based on the ideXlab platform.
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generic behavior of a piecewise Smooth Vector Field with non Smooth switching surface
arXiv: Dynamical Systems, 2016Co-Authors: Juliana Larrosa, Marco Antonio Teixeira, Tere MsearaAbstract:This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise Smooth Vector Fields when the switching set is an algebraic variety. The main focus is to obtain classification results concerning structural stability and generic codimension one bifurcations.
Hansbernd Durr - One of the best experts on this subject based on the ideXlab platform.
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a Smooth Vector Field for quadratic programming
Conference on Decision and Control, 2012Co-Authors: Hansbernd Durr, Erkin Saka, Christian EbenbauerAbstract:In this paper we consider the class of convex optimization problems with affine inequality constraints and focus hereby on the class of quadratic programs. We propose a Smooth Vector Field that is constructed such that its trajectories converge to the saddle point of the Lagrangian function associated to the convex optimization problem. We establish global asymptotic stability as well as exponential stability under mild assumptions for different variants of the Vector Field and propose a continuous-time Nesterov method.
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a Smooth Vector Field for saddle point problems
Conference on Decision and Control, 2011Co-Authors: Hansbernd Durr, Christian EbenbauerAbstract:In this paper we propose a novel Smooth Vector Field whose trajectories globally converge to the saddle point of the Lagrangian associated with a convex and constrained optimization problem. Under suitable assumptions, we prove global convergence of the trajectories for the class of strictly convex problems and we propose a Vector Field for linear programs.