Abstract
A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (nonnecessarily maximal) monotone operators by convex functions. In the finite-dimensional case, we identify the class of monotone operators that admit a convex representation as the one consisting of intersections of maximal monotone operators and characterize the monotone operators that have a unique maximal monotone extension.
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Mathematics Subject Classifications (2000)
47H05, 46B99, 47H17.
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MartÍnez-Legaz, J.E., Svaiter, B.F. Monotone Operators Representable by l.s.c. Convex Functions. Set-Valued Anal 13, 21–46 (2005). https://doi.org/10.1007/s11228-004-4170-4
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DOI: https://doi.org/10.1007/s11228-004-4170-4