Abstract
The paper suggests a new approach to calculation of subdifferentials of suprema of convex functions without any qualification conditions which essentially relies on the Hirriart-Urruty–Phelps formula for subdifferentials of sums of convex l.s.c. functions (also supplied with a simple new proof). The approach in particular provides for a simpler way to (a certain generalization of) the most recent and so far most general formulas of Hantoute–López–Zalinescu and López–Volle.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Dubovitzkii AYa, Milyutin AA (1965) Problems for extremum under constraints. Zh Vychisl Mat Mat Fiz 5:395–463 (in Russian); English transl. USSR Comput math and Math Phys 5 (1965)
Hantoute A, López M, Zǎlinescu C (2008) Subdifferential calculus rules in convex analysis: a unifying approach via pointwise supremum functions. SIAM J Optim 19:863–882
Hiriart-Urruty J-B, Moussaoui M, Seeger A, Volle M (1995) Subdifferential calculus without qualification conditions, using approximate subdifferentials. A survey. Nonlinear Anal 24:1727–1754
Hiriart-Urruty J-B, Phelps R (1993) Subdifferential calculus using ε-subdifferentials. J Funct Anal 118:154–166
López M, Volle M (2010) A formula for the set of optimal solutions of a relaxed minimization problem. Applications to the subdifferential calculus. J Convex Anal 17:1057–1075
Tikhomirov VM (1987) Analysis 2. Convex analysis and approximation theory. In: Gamkrelidze RV (ed) Encyclopedia Math sci, vol 14. Springer, Berlin
Zalinescu C (2002) Convex analysis in general vector spaces. World Scientific, Singapore
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is dedicated to Prof. Marco López on the occasion of his 60th birthday.
Rights and permissions
About this article
Cite this article
Ioffe, A.D. A note on subdifferentials of pointwise suprema. TOP 20, 456–466 (2012). https://doi.org/10.1007/s11750-011-0197-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-011-0197-5