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Convergence of Subdifferentials of Convexly Composite Functions |
Canad. J. Math. 51(1999), 250-265
Published:1999-04-01
Printed: Apr 1999
Printed: Apr 1999
- C. Combari
- R. Poliquin
- L. Thibault
Abstract
In this paper we establish conditions that guarantee, in the
setting of a general Banach space, the Painlev\'e-Kuratowski
convergence of the graphs of the subdifferentials of convexly
composite functions. We also provide applications to the
convergence of multipliers of families of constrained optimization
problems and to the generalized second-order derivability of
convexly composite functions.
| Keywords: | epi-convergence, Mosco convergence, Painlevé-Kuratowski convergence, primal-lower-nice functions, constraint qualification, slice convergence, graph convergence of subdifferentials, convexly composite functions |
| MSC Classifications: |
49A52 - unknown classification 49A52 58C06 - Set valued and function-space valued mappings [See also 47H04, 54C60] 58C20 - Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05] 90C30 - Nonlinear programming |