Characterization of Strict Convexity for Locally Lipschitz Functions

Lipschitz regularity for minima without strict convexity of the Lagrangian

We give, in a non-smooth setting, some conditions under which (some of) the minimizers of ∫ Ω f (∇u(x)) dx + g(x,u(x)) dx among the functions in W1,1(Ω) that lie between two Lipschitz functions are Lipschitz. We weaken the usual strict convexity assumption in showing that, if just the faces of the epigraph of a convex function f :Rn → R are bounded and the boundary datum u0 satisfies a generali...

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

Locally Lipschitz Functions and Bornological Derivatives

We study the relationships between Gateaux, Weak Hadamard and Fréchet differentiability and their bornologies for Lipschitz and for convex functions. AMS Subject Classification. Primary: 46A17, 46G05, 58C20. Secondary: 46B20.

On Difference Convexity of Locally Lipschitz Functions (prepared for Optimization in Honour of Alfredo Iusem’s Sixtieth Birthday)

We survey and enhance salient parts of the literature about difference convex functions with specific regard to current knowledge and applications of DC functions.

Inexactness in Bundle Methods for Locally Lipschitz Functions

We consider the problem of computing a critical point of a nonconvex locally Lipschitz function over a convex compact constraint set given an inexact oracle that provides an approximate function value and an approximate subgradient. We assume that the errors in function and subgradient evaluations are merely bounded, and in particular need not vanish in the limit. After some discussion on how t...