The Experts below are selected from a list of 98946 Experts worldwide ranked by ideXlab platform
Luciano Tubaro - One of the best experts on this subject based on the ideXlab platform.
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kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a hilbert space
arXiv: Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a Convex Set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on $\Sigma$.
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Kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a Hilbert space
Annals of Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a selfadjoint operator A and a cylindrical Wiener process on a Convex Set K with nonempty interior and regular boundary E in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on E.
Viorel Barbu - One of the best experts on this subject based on the ideXlab platform.
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kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a hilbert space
arXiv: Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a Convex Set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on $\Sigma$.
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Kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a Hilbert space
Annals of Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a selfadjoint operator A and a cylindrical Wiener process on a Convex Set K with nonempty interior and regular boundary E in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on E.
Nguyen Mau Nam - One of the best experts on this subject based on the ideXlab platform.
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Quasi-relative interiors for graphs of Convex Set-valued mappings
Optimization Letters, 2019Co-Authors: Dang Van Cuong, Boris S. Mordukhovich, Nguyen Mau NamAbstract:This paper aims at providing further studies of the notion of quasi-relative interior for Convex Sets. We obtain new formulas for representing quasi-relative interiors of Convex graphs of Set-valued mappings and for Convex epigraphs of extended-real-valued functions defined on locally Convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.
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quasi relative interiors for graphs of Convex Set valued mappings
arXiv: Optimization and Control, 2018Co-Authors: Dang Van Cuong, Boris S. Mordukhovich, Nguyen Mau NamAbstract:This paper aims at providing further studies of the notion of quasi-relative interior for Convex Sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of Convex graphs of Set-valued mappings and for Convex epigraphs of extended-real-valued functions defined on locally Convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.
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On a Convex Set with nondifferentiable metric projection
Optimization Letters, 2015Co-Authors: Shyan S. Akmal, Nguyen Mau Nam, J. J. P. VeermanAbstract:A remarkable example of a nonempty closed Convex Set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a Convex Set with \(C^{1,1}\) boundary which possesses the same property.
Giuseppe Da Prato - One of the best experts on this subject based on the ideXlab platform.
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kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a hilbert space
arXiv: Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a Convex Set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on $\Sigma$.
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Kolmogorov equation associated to the stochastic reflection problem on a smooth Convex Set of a Hilbert space
Annals of Probability, 2009Co-Authors: Viorel Barbu, Giuseppe Da Prato, Luciano TubaroAbstract:We consider the stochastic reflection problem associated with a selfadjoint operator A and a cylindrical Wiener process on a Convex Set K with nonempty interior and regular boundary E in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on E.
Zhan Kang - One of the best experts on this subject based on the ideXlab platform.
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reliability based structural optimization with probability and Convex Set hybrid models
Structural and Multidisciplinary Optimization, 2010Co-Authors: Zhan Kang, Yangjun LuoAbstract:For structural systems exhibiting both probabilistic and bounded uncertainties, it may be suitable to describe these uncertainties with probability and Convex Set models respectively in the design optimization problem. Based on the probabilistic and multi-ellipsoid Convex Set hybrid model, this paper presents a mathematical definition of reliability index for measuring the safety of structures in presence of parameter or load uncertainties. The optimization problem incorporating such reliability constraints is then mathematically formulated. By using the performance measure approach, the optimization problem is reformulated into a more tractable one. Moreover, the nested double-loop optimization problem is transformed into an approximate single-loop minimization problem by considering the optimality conditions and linearization of the limit-state function, which further facilitates efficient solution of the design problem. Numerical examples demonstrate the validity of the proposed formulation as well as the efficiency of the presented numerical techniques.
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structural reliability assessment based on probability and Convex Set mixed model
Computers & Structures, 2009Co-Authors: Zhan Kang, Alex LiAbstract:This paper investigates the reliability assessment of structures exhibiting both stochastic and bounded uncertainties by using a probability and Convex Set mixed model. The safety measure of a structure is quantified by a reliability index defined by a nested minimization problem. An iterative procedure is developed for seeking the worst-case point and the most probable failure point in the standard uncertainty space. Numerical examples are given to demonstrate the applicability of the probability and Convex Set mixed model representation in the structural reliability assessment, as well as to illustrate the validity and effectiveness of the proposed numerical method.
