Abstract

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 τaw\tau_{aw}-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 ∞\infty 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Silvia Villa

DIMA, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy

villa@dima.unige.it

Keywords

  • AW-convergence
  • well-posedness
  • optimization problems

Mathematics Subject Classification

49K40

References

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Suggested citation

S. Villa. “AW-Convergence and Well-Posedness of Non Convex Functions.” Journal of Convex Analysis 10 (2003), No. 2, 351–364. https://doi.org/10.68381/jca1020

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.