The $\mathcal U$-Lagrangian of a convex function

The U-lagrangian of a Convex Function

At a given point p, a convex function f is differentiable in a certain subspace U (the subspace along which ∂f(p) has 0-breadth). This property opens the way to defining a suitably restricted second derivative of f at p. We do this via an intermediate function, convex on U . We call this function the U-Lagrangian; it coincides with the ordinary Lagrangian in composite cases: exact penalty, semi...

The U-Lagrangian of the Maximum Eigenvalue Function

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

a structural survey of the polish posters

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Newton methods for nonsmooth convex minimization: connections among U-Lagrangian, Riemannian Newton and SQP methods

This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from U -Lagrangian theory and from Riemannian geometry. The Hessian based on the U -Lagrangian depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for...