13 papers · 1 filter
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…
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…
A note on the generalised Hessian of the least squares associated with systems of linear inequalities
M. V. Dolgopolik
The goal of this note is to point out an erroneous formula for the generalised Hessian of the least squares associated with a system of linear inequalities, that was given in the p…
The Alternating Direction Method of Multipliers for Finding the Distance between Ellipsoids
M. V. Dolgopolik
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex…
A Unified Study of Necessary and Sufficient Optimality Conditions for Minimax and Chebyshev Problems with Cone Constraints
M. V. Dolgopolik
We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First ord…