9 papers
A universal convergence theorem for primal-dual penalty and augmented Lagrangian methods
M. V. Dolgopolik
We present a so-called universal convergence theorem for inexact primal-dual penalty and augmented Lagrangian methods that can be applied to a large number of such methods and redu…
Convergence analysis of primal-dual augmented Lagrangian methods and duality theory
M. V. Dolgopolik
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagr…
Exact penalty functions and global saddle points of augmented Lagrangians for well-posed constrained optimization problems
M. V. Dolgopolik
The goal of this article is to study necessary and sufficient conditions for the exactness of penalty functions and the existence of global saddle points of augmented Lagrangians f…
An acceleration technique for methods for finding the nearest point in a polytope and computing the distance between two polytopes
M. V. Dolgopolik
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hul…
Augmented Lagrangian Functions for Cone Constrained Optimization: the Existence of Global Saddle Points and Exact Penalty Property
M. V. Dolgopolik
In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangi…
Exact augmented Lagrangians for constrained optimization problems in Hilbert spaces II: Applications
M. V. Dolgopolik
This two-part study is devoted to the analysis of the so-called exact augmented Lagrangians, introduced by Di Pillo and Grippo for finite dimensional optimization problems, in the…