Results 1 to 10 of about 1,290,281 (292)
Directional Metric Regularity of Multifunctions [PDF]
Mathematics of Operations Research, 2015 In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings.
Michel Thera, Huynh Van Ngai
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Directional Hölder Metric Regularity
Journal of Optimization Theory and Applications, 2015 This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder /Lipschitz metric regularity is stable, when the multifunction under consideration ...
Michel Thera +2 more
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Metric Regularity of the Sum of Multifunctions and Applications [PDF]
Journal of Optimization Theory and Applications, 2013 In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical multifunctions. Our results subsume some recent results by Durea and Strugariu.
Michel Thera +2 more
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The Radius of Metric Regularity Revisited [PDF]
Set-Valued and Variational Analysis, 2023 AbstractThe paper extends the radius of metric regularity theorem by Dontchev, Lewis and Rockafellar (2003) by providing an exact formula for the radius with respect to Lipschitz continuous perturbations in general Asplund spaces, thus, answering affirmatively an open question raised twenty years ago by Ioffe. In the non-Asplund case, we give a natural
Helmut Gfrerer, Alexander Y. Kruger
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A regular metric does not ensure the regularity of spacetime [PDF]
The European Physical Journal Plus, 2023 In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There is work in the literature that assumes that the regularity of the metric is a sufficient condition to guarantee ...
Manuel E. Rodrigues, Henrique A. Vieira
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Metric Regularity Relative to a Cone
Vietnam Journal of Mathematics, 2019 Metric regularity and related properties are powerful tools for dealing with problems of optimization and variational analysis, and its has a long history. Important applications enclose the study of stability of variational systems as well as convergence of Newton's type methods.
Huynh Van Ngai +2 more
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Directional Regularity and Metric Regularity
SIAM Journal on Optimization, 2007 For general constraint systems in Banach spaces, we present the directional stability theorem based on the appropriate generalization of the directional regularity condition, suggested earlier in [A. V. Arutyunov and A. F. Izmailov, Math. Oper. Res., 31 (2006), pp. 526-543].
Aram Arutyunov +2 more
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Local convergence of quasi-Newton methods under metric regularity
Computational Optimization and Applications, 2013 We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence.
Anton Belyakov +2 more
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Regularity and numerical approximation of fractional elliptic differential equations on compact metric graphs [PDF]
Mathematics of Computation, 2023 The fractional differential equation $L^\beta u = f$ posed on a compact metric graph is considered, where $\beta>0$ and $L = \kappa^2 - \nabla(a\nabla)$ is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth ...
D. Bolin +3 more
semanticscholar +1 more source
Asymptotic stationarity and regularity for nonsmooth optimization problems [PDF]
Journal of Nonsmooth Analysis and Optimization, 2020 Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this new sense are
Patrick Mehlitz
doaj +1 more source