On a sufficient condition for equality of two maximal monotone operators

Host Institution:

University of South Australia

Title of Seminar:

On a sufficient condition for equality of two maximal monotone operators

Speaker's Name:

Assoc. Prof. Regina S. Burachik

Speaker's Institution:

University of South Australia

Time and Date:

Wednesday 28 April 2010 at 2:00 pm Sydney time (1:30 pm Adelaide time)

Seminar Abstract:

 

The first part of the talk is an introduction to enlargements of maximal monotone operators and some related theory. In the second part of the talk we establish minimal conditions under which two maximal monotone operators coincide. Our first result is inspired by an analogous result for subdifferentials of convex functions. In particular, we prove that two maximal monotone operators T, S which share the same convex-like domain D coincide whenever T(x) intersects S(x) for every x in D. We extend our result to the setting of enlargements of maximal monotone operators. More precisely, we prove that two operators coincide as long as the enlargements have nonempty intersection at each point of their common domain, the latter set assumed to be convex-like (a condition weaker than convexity) and open. We then use this result to obtain new facts for convex functions: we show that the difference of two convex functions whose subdifferentials have a common open convex-like domain is constant if and only if their epsilon-subdifferentials intersect at every point of that domain. 

The new results presented in the second part of the talk are joint work with Juan Enrique Martinez-Legaz (Autonomous University of Barcelona) and Marco Rocco (Universita degli Studi di Bergamo).

 

 

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