Lipschitz programming via increasingconvex - along - rays functions

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

Online Supplement to “Resource Allocation via Message Passing”

Proof. Let L be a Lipschitz constant that applies to all utility functions. Suppose each message in the set V is Lipschitz continuous with Lipschitz constant L. Consider the message from an activity a to a resource r ∈ R(a). Define X a\r , ∏r∈R(a)\r Xr to be the space of consumption bundles for activity a, excluding resource r. Without loss of generality, assume that (FV )a→r(xar) ≥ (FV )a→r(xa...

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Weighted composition operators between Lipschitz algebras of complex-valued bounded functions

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.