Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

Ioffe, Alexander, and Penot, Jean-Paul. "Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings." Serdica Mathematical Journal 22.3 (1996): 359-384. <http://eudml.org/doc/11642>.

@article{Ioffe1996,
abstract = {The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.},
author = {Ioffe, Alexander, Penot, Jean-Paul},
journal = {Serdica Mathematical Journal},
keywords = {Set-Valued Mapping; Lower Semicontinuous Function; Subdifferential; Normal Cone; Coderivative; Marginal Function; lower semicontinuous functions; subdifferentials; coderivatives; set-valued mappings},
language = {eng},
number = {3},
pages = {359-384},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings},
url = {http://eudml.org/doc/11642},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Ioffe, Alexander
AU - Penot, Jean-Paul
TI - Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 3
SP - 359
EP - 384
AB - The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.
LA - eng
KW - Set-Valued Mapping; Lower Semicontinuous Function; Subdifferential; Normal Cone; Coderivative; Marginal Function; lower semicontinuous functions; subdifferentials; coderivatives; set-valued mappings
UR - http://eudml.org/doc/11642
ER -