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Abstract
We study the relations for quasiconcave and continuous functions between the two important notions of Clarke and Greenberg-Pierskalla differentiability. As an application, we generalize the classic Roy's identity of consumer theory.
Author information
Contact details are reproduced from the original publication and may be historical.
SC
Simone Cerreia-Vioglio
Department of Decision Sciences, Università Bocconi, Milano, Italy
Department of Decision Sciences, Università Bocconi, Milano, Italy
MM
Massimo Marinacci
Department of Decision Sciences, Università Bocconi, Milano, Italy
LM
Luigi Montrucchio
Collegio Carlo Alberto, Università di Torino, Torino, Italy
Keywords
Clarke differential
Greenberg-Pierskalla differential
directionally Lipschitzian
quasiconcave function
max-formula
envelope theorem
affine Gateaux differentiability
Mathematics Subject Classification
26B25, 26E15, 90C26, 49J52
Suggested citation
S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci, L. Montrucchio. “On the Equality of Clarke and Greenberg-Pierskalla Differentials.” Journal of Convex Analysis 29 (2022), No. 2, 459–480.