Results 151 to 160 of about 1,294 (187)

Lower Semicontinuity of Marginal Functions

1984
Criteria for the lower semicontinuity of marginal functions constitute one of the most important topics of optimization.
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Lower semicontinuous convex functions

1989
Our differentiability results for convex functions made heavy and consistent use of continuity, but in both theoretical and applied aspects of convex functions, it is sometimes desirable to weaken this hypothesis. Lower semicontinuity is precisely what is needed.
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Lower semicontinuity of A class of functionals in SBV H

Applied Mathematics-A Journal of Chinese Universities, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song, Yingqing, Yang, Xiaoping, Long, Fei   +2 more
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Points of Upper and Lower Semicontinuity for Multivalued Functions

Ukrainian Mathematical Journal, 2018
It is known that a multifunction of two variables $F:X\times Y\to Z$, whose $X$ and $Y$ sections are both lower (resp. upper) semicontinuous may be (under usual assumptions on $X$, $Y$, $Z$) non weakly measurable (resp. nonmeasurable), but if the $X$-sections are lsc, the $Y$-sections are usc and the values are compact, it belongs to the upper Borel ...
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Lower Semicontinuity Conditions for Functionals on Jumps and Creases

SIAM Journal on Mathematical Analysis, 1995
Summary: A class of functionals of the form \[ {\mathcal F} (u) = \int_I \bigl |u''(t) \bigr |^2dt + \int_I |u - g |^2 dt + \sum_{t \in S} \varphi \bigl( t,u(t_-), u(t_+),\;u'(t_-),\;u'(t_+) \bigr), \] defined on piecewise \(H^2\) functions is studied, where \(S\) is the union of the set of points of discontinuity for \(u\) and the set of points of ...
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Lower semicontinuous Lyapunov functions and subdifferential calculus

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2003
We show that lower semicontinuous Lyapunov functions can be used to determine both stable and attractive sets of differential equations with a short proof similar to that of the original Lyapunov indirect method. Several examples illustrate the flexibility of using such lower semicontinuous Lyapunov functions.
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Conjugacies adapted to lower semicontinuous functions

Optimization, 2013
AbstractWe revisit a remarkable duality devoted to lower semicontinuous functions. We compare its definition in terms of a coupling with its definition in terms of linear-like (or elementary) functions. We consider several variants. Then, we deal with the passage from smoothness to rotundity and the reverse passage and we examine the transfer of ...
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Generalized convexities of lower semicontinuous functions

Optimization, 1985
In this paper a general theorem on the replacement of the condition “for all λ” in the definition of generalized convexity properties of lower semicontinuous functions by the condition “there exists a λ” is shown. This result can be applied to a number of special kinds of convexity and completes, for instance, studies of Behbikgeb concerning ...
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Weak lower semicontinuity of integral functionals

Journal of Optimization Theory and Applications, 1976
A lower semicontinuity theorem for integral functionals is proved underL1-strong convergence of the trajectories andL1-weak convergence of the control functions. An alternative statement is also proved under pointwise convergence of the trajectories.
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Lower Semicontinuous Functionals

2005
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