Your selections:

10101 Pure Mathematics
10103 Numerical and Computational Mathematics
1Additive enlargements
1Approximation properties
1Brøndsted- Rockafellar enlargements
1Convex lower semicontinuous function
1Downward subsets
1Enlargement of an operator
1Fenchel-Young function
1Fitzpatrick function
1Maximally monotone operator
1Subdifferential operator
1ε-subdifferential mapping

Show More

Show Less

Format Type

An additive subfamily of enlargements of a maximally monotone operator

- Burachik, Regina, Martinez-Legaz, Juan, Rezaie, Mahboubeh, Thera, Michel

**Authors:**Burachik, Regina , Martinez-Legaz, Juan , Rezaie, Mahboubeh , Thera, Michel**Date:**2015**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 643-665**Full Text:****Reviewed:****Description:**We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical epsilon-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the epsilon-subdifferential enlargement.

**Authors:**Burachik, Regina , Martinez-Legaz, Juan , Rezaie, Mahboubeh , Thera, Michel**Date:**2015**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 643-665**Full Text:****Reviewed:****Description:**We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical epsilon-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the epsilon-subdifferential enlargement.

Downward sets and their separation and approximation properties

- Martinez-Legaz, Juan, Rubinov, Alex, Singer, Ivan

**Authors:**Martinez-Legaz, Juan , Rubinov, Alex , Singer, Ivan**Date:**2002**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 23, no. 2 (Jun 2002), p. 111-137**Full Text:**false**Reviewed:****Description:**We develop a theory of downward subsets of the space R-I, where I is a finite index set. Downward sets arise as the set of all solutions of a system of inequalities x is an element of R-I, f(t)(x) less than or equal to 0 (t is an element of T), where T is an arbitrary index set and each f(t) (t is an element of T) is an increasing function defined on R-I. These sets play an important role in some parts of mathematical economics and game theory. We examine some functions related to a downward set (the distance to this set and the plus-Minkowski gauge of this set, which we introduce here) and study lattices of closed downward sets and of corresponding distance functions. We discuss two kinds of duality for downward sets, based on multiplicative and additive min-type functions, respectively, and corresponding separation properties, and we give some characterizations of best approximations by downward sets. Some links between the multiplicative and additive cases are established.**Description:**2003000119

- «
- ‹
- 1
- ›
- »

Are you sure you would like to clear your session, including search history and login status?