140 citations · 174 across the 14 of their papers we have counts for
6 papers · 1 filter
Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
Jonathan M. Borwein, Liangjin Yao
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qua…
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…
Legendre-type integrands and convex integral functions
Jonathan M. Borwein, Liangjin Yao
In this paper, we study the properties of integral functionals induced on by closed convex functions on a Euclidean space . We give sufficient conditions for such…
Construction of pathological maximally monotone operators on non-reflexive Banach spaces
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Brøns…
Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question po…
For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint
Heinz H. Bauschke, Jonathan M. Borwein, Xianfu Wang +1
It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick-Phelps t…