An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming

A Feasible Augmented Lagrangian Method for Non-lipschitz Nonconvex Programming

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

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

A Quadratic Approximation Method Based on Augmented Lagrangian Functions for Nonconvex Nonlinear Programming Problems

Convergence Results on Proximal Method of Multipliers in Nonconvex Programming

We describe a primal-dual application of the proximal point algorithm to nonconvex minimization problems. Motivated by the work of Spingarn and more recently by the work of Kaplan and Tichatschke about the proximal point methodology in nonconvex optimization. This paper discusses some local results in two directions. The first one concerns the application of the proximal method of multipliers t...

An Augmented Lagrangian Based Algorithm for Distributed NonConvex Optimization

This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interprete...