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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,

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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