Results 11 to 20 of about 9,586,445 (221)
Characterization of lower semicontinuous convex functions [PDF]
Proceedings of the American Mathematical Society, 1992 We prove that a lower semicontinuous function defined on a reflexive Banach space is convex if and only if its Clarke subdifferential is monotone.
Correa, R., Jofré, A., Thibault, L.
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Some characterizations of error bound for non-lower semicontinuous functions
Journal of Inequalities and Applications, 2019 In this paper, we study the error bound of non-lower semicontinuous functions. First, we extend the concepts of strong slope and global slope to the non-lower semicontinuous functions.
Miantao Chao +2 more
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Topological Spaces and Lattices of Lower Semicontinuous Functions [PDF]
Transactions of the American Mathematical Society, 1973 Lower semicontinuous real-valued functions on a space X X form a conditionally complete distributive lattice
M. C. Thornton
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On error bounds for lower semicontinuous functions
Mathematical Programming, 2002 This paper refines earlier results from [\textit{K. F. Ng, X. Y. Zheng}, SIAM J. Optim. 12, No. 1, 1--17 (2001; Zbl 1040.90041)] on error bounds for lower semicontinuous functions \(f:X\rightarrow {\mathbb R}\) defined on a metric space \(X.\) In particular, the authors consider error bounds with exponent \(\beta >0,\) in which the distance from \(x\in
Zili Wu, Jane J. Ye
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On the Lower Semicontinuity of Supremal Functionals [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2003 Summary: In this paper we study the lower semicontinuity problem for a supremal functional of the form \[ F(u,\Omega )= \underset {x\in \Omega } {\text{ess\,sup}} f(x,u(x),Du(x)) \] with respect to the strong convergence in \(L^\infty (\Omega )\), furnishing a comparison with the analogous theory developed by Serrin for integrals.
GORI, MICHELE, MAGGI, FRANCESCO
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Weak Lower Semicontinuity of Integral Functionals and Applications [PDF]
SIAM Review, 2017 Minimization is a reoccurring theme in many mathematical disciplines ranging from pure to applied ones. Of particular importance is the minimization of integral functionals that is studied within the calculus of variations. Proofs of the existence of minimizers usually rely on a fine property of the involved functional called weak lower semicontinuity.
Barbora Benesová, Martin Kruzík
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On the ARG MIN multifunction for lower semicontinuous functions [PDF]
Proceedings of the American Mathematical Society, 1988 The epi-topology on the lower semicontinuous functions L ( X )
Beer, Gerald, Kenderov, Petar
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Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD [PDF]
Journal of Functional Analysis, 2021 In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix.
Friedrich M., Perugini M., Solombrino F.
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Lower semicontinuity and relaxation of nonlocal $$L^\infty $$-functionals [PDF]
Calculus of Variations and Partial Differential Equations, 2020 AbstractWe study variational problems involving nonlocal supremal functionals$$\begin{aligned} L^\infty (\Omega ;{\mathbb {R}}^m) \ni u\mapsto \mathrm{ess sup}_{(x,y)\in \Omega \times \Omega } W(u(x), u(y)), \end{aligned}$$L∞(Ω;Rm)∋u↦esssup(x,y)∈Ω×ΩW(u(x),u(y)),where$$\Omega \subset \mathbb {R}^n$$Ω⊂Rnis a bounded, open set and$$W:\mathbb {R}^m\times ...
Carolin Kreisbeck, Elvira Zappale
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Nonconvex, lower semicontinuous piecewise linear optimization [PDF]
, 2008 A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem.
Vielma, Juan Pablo +2 more
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