6533b862fe1ef96bd12c696b

RESEARCH PRODUCT

Subdifferential and conjugate calculus of integral functions with and without qualification conditions

Abderrahim HantouteAbderrahim Jourani

subject

Subdifferentialsconvex normal integrandsConvex normal integrandsSuslin spacessub-differentialsSuslin spaces. Mathematics Subject Classi…cation (2010): 26B0526J25[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]49H05Integral functions and functionals

description

We characterize the subdifferential and the Fenchel conjugate of convex integral functions by means of respectively the approximate subdifferential and the conjugate of the associated convex normal integrands. The results are stated in Suslin locally convex spaces, and do not require continuity-type qualification conditions on the functions, nor special topological or algebraic structures on the index set. Consequently, when confined to separable Banach spaces, the characterizations of such a subdifferential are obtained using only the exact subdifferential of the given integrand but at nearby points. We also provide some simplifications of our formulas when additional continuity conditions are in force. Research of the first author was supported by MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA-GAL 18/00205), and by Projects PGC2018-097960-B-C21 from MICINN of Spain and AICO/2021/165 of Generalitat, Valenciana, and by ANID Fondecyt 1190012. The work of the second author was partially supported by the EIPHI Graduate School (contract ANR-17-EURE-0002).

yearjournalcountryeditionlanguage
2023-01-01
https://hal.science/hal-03672604