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Sur un principe géométrique en analyse convexe

Andrzej GranasMarc Lassonde — 1991

Studia Mathematica

In this note we present we present a new elementary approach in the theory of minimax inequalities. The proof of the main result (called the geometric principle) uses only some simple properties of convex functions. The geometric principle (which is equivalent to the well-known lemma of Klee [13]) is shown to have numerous applications in different areas of mathematics.

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

Jules, FlorenceLassonde, Marc — 2010

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09. We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as...

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