Monotone Operators Representable by l.s.c. Convex Functions |
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Authors: | J -E MartÍnez-Legaz and B F Svaiter |
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Institution: | (1) CODE and Departament dEconomia i dHistòria Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain;(2) IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, RJ, Brasil |
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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.Mathematics Subject Classifications (2000) 47H05, 46B99, 47H17. |
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Keywords: | monotone operators convex functions |
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