On Lipschitz optimization based on gray-box piecewise linearization

On stable piecewise linearization and generalized algorithmic differentiation

It is shown how functions that are defined by evaluation programs involving the absolute value function abs() (besides smooth elementals), can be approximated locally by piecewise-linear models in the style of algorithmic, or automatic, differentiation (AD). The model can be generated by a minor modification of standard AD tools [GJU96b] and it is Lipschitz continuous with respect to the base p...

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

Geometry and Combinatorics of the Cutting Angle Method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of ma...

New approach for attenuation correction in SPECT images, using linear optimization

Background: Photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of SPECT images and results to errors in accuracy of quantitative measurements. This can be corrected via different physical or mathematical approaches. As the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘Piece ...

Non-Lipschitz lp-Regularization and Box Constrained Model for Image Restoration

Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant θ for using nonconvex nonsmooth regularizat...