17 citations · 148 across the 28 of their papers we have counts for
28 papers
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…
Subdifferentials of convex matrix-valued functions
M. V. Dolgopolik
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on that are convex with respect to the Löwner partial order can have a complica…
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…
Hypodifferentials of nonsmooth convex functions and their applications to nonsmooth convex optimization
M. V. Dolgopolik
A hypodifferential is a compact family of affine mappings that defines a local max-type approximation of a nonsmooth convex function. We present a general theory of hypodifferentia…
An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints
M. V. Dolgopolik
A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control…
Nonlocal error bounds for piecewise affine functions
M. V. Dolgopolik
The paper is devoted to a detailed analysis of nonlocal error bounds for nonconvex piecewise affine functions. We both improve some existing results on error bounds for such functi…
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…
Exact augmented Lagrangians for constrained optimization problems in Hilbert spaces I: Theory
M. V. Dolgopolik
In this two-part study, we develop a general theory of the so-called exact augmented Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to traditional…
Steering exact penalty DCA for nonsmooth DC optimization problems with equality and inequality constraints
M. V. Dolgopolik
We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the penalty function for solving nonsmooth DC optimization problems with nonsmoo…
Exact penalty functions with multidimensional penalty parameter and adaptive penalty updates
M. V. Dolgopolik
We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison w…
Codifferentials and Quasidifferentials of the Expectation of Nonsmooth Random Integrands and Two-Stage Stochastic Programming
M. V. Dolgopolik
This work is devoted to an analysis of exact penalty functions and optimality conditions for nonsmooth two-stage stochastic programming problems. To this end, we first study the co…
DC Semidefinite Programming and Cone Constrained DC Optimization: Theory and Local Search Methods
M. V. Dolgopolik
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general…
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…
A New Constraint Qualification and Sharp Optimality Conditions for Nonsmooth Mathematical Programming Problems in Terms of Quasidifferentials
M. V. Dolgopolik
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming proble…
Exact Penalty Functions for Optimal Control Problems II: Exact Penalisation of Terminal and Pointwise State Constraints
M. V. Dolgopolik
The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstr…
Exact Penalty Functions for Optimal Control Problems I: Main Theorem and Free-Endpoint Problems
M. V. Dolgopolik, A. V. Fominyh
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal an…
Metric Regularity of Quasidifferentiable Mappings and Optimality Conditions for Nonsmooth Mathematical Programming Problems
M. V. Dolgopolik
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new nec…
Speed-Gradient Control of the Brockett Integrator
M. V. Dolgopolik, A. L. Fradkov
A nonsmooth extension of the speed-gradient algorithms in finite form is proposed. The conditions ensuring control goal (convergence of the goal function to zero) are established.…
Abstract convex approximations of nonsmooth functions
M. V. Dolgopolik
In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codiffe…
New global optimality conditions for nonsmooth DC optimization problems
M. V. Dolgopolik
In this article we propose a new approach to an analysis of DC optimization problems. This approach was largely inspired by codifferential calculus and the method of codifferential…