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Journal of Convex Analysis 10 (2003), No. 2, 351--364
Copyright Heldermann Verlag 2003
AW-Convergence and Well-Posedness of Non Convex Functions
Silvia Villa
DIMA, Universita di Genova, Via Dodecaneso 35, 16146 Genova, Italy,
villa@dima.unige.it
We consider the set of lower semicontinuous functions defined on a
Banach space, equipped with AW-convergence. A function is called Tikhonov
well-posed provided it has a unique minimizer to which every minimizing
sequence converges. We show that well-posedness of f guarantees strong
convergence of approximate minimizers of taw
-approximating functions (under conditions of equiboundedness of sublevel
sets), to the minimizer of f. Moreover we show that a lower semicontinuous
function f which satisfies growth conditions at infinity is well-posed iff
its lower semicontinuous convex regularization is. Finally we investigate
the link between AW-convergence of non convex integrands and that of the
associated integral functionals.
Keywords: AW-convergence, well-posedness, optimization problems.
MSC 2000: 49K40.
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