Results 141 to 150 of about 1,294 (187)

Error Bounds for Lower Semicontinuous Functions in Normed Spaces

SIAM Journal on Optimization, 2001
Summary: Without the convexity or analyticity assumption, we study error bounds for an inequality system defined by a general lower semicontinuous function and establish sufficient/necessary conditions on the existence of error bounds in infinite dimensional normed spaces.
Xi Yin Zheng, Kung Fu Ng
exaly   +2 more sources

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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Convex and Lower-Semicontinuous Functions

2021
In this chapter, one section is about convex functions and their properties. Another section is about lower-semicontinuous functions and their properties in compact topological spaces and in Banach spaces. The final section presents some properties of functions that are both convex and lower-semicontinuous. More precisely, some conditions are discussed
Adina Chirilă, Marin Marin, Andreas Öchsner   +2 more
openaire   +1 more source

Convex and Lower Semicontinuous Functionals

2021
In this chapter we briefly present basic properties of convex functions (as the Lipschitz property of convex functionals, the definition and main properties of the conjugate of a convex functional and the convex subdifferential), the direct method in the calculus of variations as well as the variational principle of Ekeland.
Nicuşor Costea, Alexandru Kristály, Csaba Varga   +2 more
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On Lower Semicontinuity of Integral Functionals. II

SIAM Journal on Control and Optimization, 1977
A necessary and sufficient condition for the integral functional $I(x( \cdot ),y( \cdot )) = \smallint _G f(t,x(t),y(t))d\mu $ to be sequentially lower semicontinuous with respect to some kinds of strong convergence of $x( \cdot )$components and weak convergence of $y( \cdot )$-components is proved.
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On the Cone of Bounded Lower Semicontinuous Functions

Mathematical Notes, 2005
For a topological space \(X\), let \(BC(X)\) be the Banach space of all bounded, real-valued continuous functions on \(X\), endowed with the ordinary addition and multiplication and the partial order: \[ f_1\geq f_2\quad\text{iff }f_1(x)\geq f_2(x)\quad\text{for all }x\in X, \] and the sup-norm \(\| f\|= \sup\{|f(x)|: x\in X\}\). \(BC(X)_\sim\) denotes
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Lower Semicontinuity Properties of Functionals with Free Discontinuities

Archive for Rational Mechanics and Analysis, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francesco Maddalena, Sergio Solimini
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Lower Semicontinuous Convex Functions

2011
The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
Heinz H. Bauschke, Patrick L. Combettes
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L 2-lower semicontinuity of functionals of quadratic type

Annali di Matematica Pura ed Applicata, 1981
A representation formula for the L2-lower semicontinuous envelope of a quadratic integral of Calculus of Variations is given. Some particular cases are explicited in the details.
FUSCO, NICOLA, MOSCARIELLO, GIOCONDA
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Lower Semicontinuous Increasing Functionals

1993
In this chapter we study some properties of the functionals F(x,A) which are lower semicontinuous with respect to x and increasing with respect to A.
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