Inexactness in Bundle Methods for Locally Lipschitz Functions

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

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

Nonsmooth Trust Region Algorithms for Locally Lipschitz Functions on Riemannian Manifolds

This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function Φ : TM → R on the tangent bundle TM , and at k-th iteration, using the restricted function Φ|TxkM where TxkM is the tangent space at xk, a local model function Qk that carries both fi...

Bundle method for non-convex minimization with inexact subgradients and function values∗

We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points.

A secant method for nonsmooth optimization

The notion of a secant for locally Lipschitz continuous functions is introduced and a new algorithm to locally minimize nonsmooth, nonconvex functions based on secants is developed. We demonstrate that the secants can be used to design an algorithm to find descent directions of locally Lipschitz continuous functions. This algorithm is applied to design a minimization method, called a secant met...