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pro vyhledávání: '"Dolgopolik, M. V."'
Autor:
Dolgopolik, M. V.
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal is to pre
Externí odkaz:
http://arxiv.org/abs/2409.13974
Autor:
Dolgopolik, M. V.
Publikováno v:
Optimization Methods and Software (2024)
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 paper "A finite Newton method for classification" by O.L. Mangasarian (
Externí odkaz:
http://arxiv.org/abs/2404.15571
Autor:
Dolgopolik, M. V.
Publikováno v:
Optimization Letters (2024)
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\mathbb{R}^d$ that are convex with respect to the L\"{o}wner partial order can have a complicated structure and might be very difficult to compute even in simpl
Externí odkaz:
http://arxiv.org/abs/2307.15856
Exact augmented Lagrangians for constrained optimization problems in Hilbert spaces II: Applications
Autor:
Dolgopolik, M. V.
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 case of optimization problems in Hilbert spaces. In the second part of
Externí odkaz:
http://arxiv.org/abs/2305.03897
Autor:
Dolgopolik, M. V.
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 hypodifferentials of nonsmooth convex functions defined on a Banach space. In particu
Externí odkaz:
http://arxiv.org/abs/2303.13464
Autor:
Dolgopolik, M. V.
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 constraints is presented, in which the the penalty parameter and seve
Externí odkaz:
http://arxiv.org/abs/2302.09343
Autor:
Dolgopolik, M. V.
Publikováno v:
Set-Valued and Variational Analysis, vol. 31, article number 32, (2023)
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 functions and present completely new necessary and/or sufficient conditions
Externí odkaz:
http://arxiv.org/abs/2210.02606
Autor:
Dolgopolik, M. V.
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 hull of a finite number of points, in the case when the number of points
Externí odkaz:
http://arxiv.org/abs/2205.04553
Autor:
Dolgopolik, M. V.
Publikováno v:
Optimization, 73:5 (2024) 1355-1395
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 nonsmooth exact penalty functions, these augmented Lagrangians are co
Externí odkaz:
http://arxiv.org/abs/2201.12254
Autor:
Dolgopolik, M. V.
Publikováno v:
Optimization Methods and Software, 38:4 (2023) 668-697
We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the $\ell_1$ penalty function for solving nonsmooth DC optimization problems with nonsmooth DC equality and inequality constraints. The method employs an adapt
Externí odkaz:
http://arxiv.org/abs/2107.01433