9 papers
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…