论文信息 - Monotone Operators Representable by l.s.c. Convex Functions

Monotone Operators Representable by l.s.c. Convex Functions

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.

B. Svaiter | J. Martínez-Legaz

[1] R. Rockafellar,et al. On the maximal monotonicity of subdifferential mappings. , 1970 .

[2] H. Brezis. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[3] H. Brezis. Analyse fonctionnelle : théorie et applications , 1983 .

[4] S. Fitzpatrick. Representing monotone operators by convex functions , 1988 .

[5] R. Phelps. Convex Functions, Monotone Operators and Differentiability , 1989 .

[6] P. D. Tao,et al. Partial regularization of the sum of two maximal monotone operators , 1993 .

[7] A. Iusem,et al. Enlargement of Monotone Operators with Applications to Variational Inequalities , 1997 .

[8] S. Simons. Minimax and monotonicity , 1998 .

[9] Michel Théra,et al. Ill-posed Variational Problems and Regularization Techniques , 1999 .

[10] Variational and Extended Sums of Monotone Operators , 1999 .

[11] M. Théra,et al. Generalized sums of monotone operators , 1999 .

[12] Benar Fux Svaiter,et al. A Family of Enlargements of Maximal Monotone Operators , 2000 .

[13] Abdellatif Moudafi,et al. On the regularization of the sum of two maximal monotone operators , 2000 .

[14] Benar Fux Svaiter,et al. Maximal Monotone Operators, Convex Functions and a Special Family of Enlargements , 2002 .

[15] Juan Enrique Martínez-Legaz,et al. A CONVEX REPRESENTATION OF MAXIMAL MONOTONE OPERATORS , 2003 .