92 citations · 106 across the 19 of their papers we have counts for
7 papers · 1 filter
A Note on Carlier Inequality
Regina S. Burachik, J. E. Martínez-Legaz
Recently, Carlier established in [3] a quantitave version of the Fitzpatrick inequality in a Hilbert space. We extend this result by Carlier to the framework of reflexive Banach sp…
Generalized Bregman envelopes and proximity operators
Regina S. Burachik, Minh N. Dao, Scott B. Lindstrom
Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, B…
Zero Duality Gap in View of Abstract Convexity
Hoa T. Bui, Regina S. Burachik, Alexander Y. Kruger +1
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical…
The Generalized Bregman Distance
Regina S. Burachik, Minh N. Dao, Scott B. Lindstrom
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a prop…
Conditions for zero duality gap in convex programming
Jonathan M. Borwein, Regina S. Burachik, Liangjin Yao
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constrain…
Monotone Operators without Enlargements
Jonathan M. Borwein, Regina Burachik, Liangjin Yao
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original map…
Maximal monotonicity, conjugation and the duality product
Regina Sandra Burachik, B. F. Svaiter
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator a…