Locally Lipschitz Functions and Bornological Derivatives

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

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.

Nonsmooth Equations in Optimization Nonconvex Optimization and Its Applications

The titles published in this series are listed at the end of this volume. 1 1 2 4 4 4 5 5 6 6 7 9 Multifunctions and Derivatives Particular Locally Lipschitz Functions and Related Definitions Generalized Jacobians of Locally Lipschitz Functions Pseudo-Smoothness and D°f Piecewise Functions NCP Functions 1.4 Definitions of Regularity Definitions of Lipschitz Properties Regularity Definitions Fun...

POINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

Bornological Quantum Groups

We introduce and study the concept of a bornological quantum group. This generalizes the theory of algebraic quantum groups in the sense of van Daele from the algebraic setting to the framework of bornological vector spaces. Working with bornological vector spaces, the scope of the latter theory can be extended considerably. In particular, the bornological theory covers smooth convolution algeb...