Convex cones of generalized multiply monotone functions and the dual cones

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

Adaptive, anisotropic and hierarchical cones of discrete convex functions

We introduce a new class of adaptive methods for optimization problems posed on the cone of convex functions. Among the various mathematical problems which posses such a formulation, the Monopolist problem [24, 10] arising in economics is our main motivation. Consider a two dimensional domain Ω, sampled on a grid X of N points. We show that the cone Conv(X) of restrictions to X of convex functi...

Second Order Cones for Maximal Monotone Operators via Representative Functions

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T , in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the GraphT . In particular we obtain formula for the Proto-derivative, as well as its polar, the normal cone to the grap...

Some Results on Boundedness in Locally Convex Cones