arXiv subjects

A. A. Titov

Publications and source records attributed to A. A. Titov.

6 recordsLinked to original sources

arXiv2022

Some Adaptive First-order Methods for Variational Inequalities with Relatively Strongly Monotone Operators and Generalized Smoothness

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical method for generalized smooth (with Hölder condition) saddle point problem, which has convergence rate estimates similar to accelerated methods. We provide the motivation for such an approach and obtain theoretical results of the proposed method. Our second focus is the adaptation of widespread recently proposed methods for solving variational inequalities with relatively strongly monotone operators. The key idea in our approach is the refusal of the well-known restart technique, which in some cases causes difficulties in implementing such algorithms for applied problems. Nevertheless, our algorithms show a comparable rate of convergence with respect to algorithms based on the above-mentioned restart technique. Also, we present some numerical experiments, which demonstrate the effectiveness of the proposed methods. [1] Jin, Y., Sidford, A., & Tian, K. (2022). Sharper rates for separable minimax and finite sum optimization via primal-dual extragradient methods. arXiv preprint arXiv:2202.04640.

math.OC↗

arXiv2022

Some Methods for Relatively Strongly Monotone Variational Inequalities

The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz condition of the operator that appeared several years ago. One of these classes is associated with the relative boundedness of the operator, and the other one with the analog of the Lipschitz condition (namely, relative smoothness). For variational inequalities with relatively bounded and relatively strongly monotone operators, we introduce a modification of the Mirror Descent method, which optimizes the convergence rate. We also propose the adaptive Proximal Pirror algorithm and its restarted version with a linear convergence rate for problems with relatively smooth and relatively strongly monotone operators.

math.OC↗

arXiv2021

The crystal structure, chemical bonding and magnetic properties of the intercalation compounds Cr$_x$ZrTe$_2$ ($x$ = 0-0.3)

New intercalation compounds Cr$_x$ZrTe$_2$ were synthesized in the Cr concentration range of x=0-0.3. A thorough study of the crystal and electronic structure has been performed. It was found that there is competition in the distribution of the Cr atoms over the octa- and tetrahedral sites in the van der Waals gap, depending on the Cr content. The ordering of the Cr atoms was found at x = 0.25; at the same time, the lattice symmetry decreases from trigonal P-3m1 to monoclinic F2/m. This ordering stabilizes the octahedral coordination of the Cr atoms by Te atoms. The analysis of the experimental data on the electronic structure and DOS calculations showed that the Cr 3d states are spin-split.

cond-mat.mtrl-sci↗

arXiv2018

On Some Adaptive Mirror Descent Algorithms for Convex and Strongly Convex Optimization Problems with Functional Constraints

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are applicable to the objective functionals of various level of smoothness: the Lipschitz condition is valid either for the objective functional itself or for its gradient or Hessian (and the functional may not satisfy the Lipschitz condition). By using the restart technique methods for strongly convex minimization problems are proposed. Estimates of the rate of convergence of the considered algorithms are obtained depending on the level of smoothness of the objective functional. Numerical experiments illustrating the advantages of the proposed methods for some examples are presented.

math.OC↗

arXiv2015

The electronic structure formation of CuxTiSe2 in a wide range (0.04 < x < 0.8) of copper concentration

An experimental study of the electronic structure of copper intercalated titanium dichalcogenides in a wide range of copper concentrations (x = 0.05 - 0.6) using the x-rays photoemission spectroscopy, resonant photoemission and x-rays absorption spectroscopy has been performed. Negative energy shifts of the Ti 2p and Se 3d core levels spectra and a corresponding decrease of the photon energy in Ti 2p absorption spectra with increasing concentration of copper have been found. Such sign-anomalous shifts may be explained by the shielding effect of the corresponding atomic shells as a result of the dynamic charge transfer during the formation of a covalent chemical bond between the copper atoms and the TiSe2 matrix.

cond-mat.mtrl-sci↗

arXiv2009

Synthesis, crystal growth and superconducting properties of Fe-Se system

Single crystals FeSex were grown in an evacuated sealed quartz tube using polycrystalline material by gas-transport reaction with I2 as a gas-carrier. Crystals with hexagonal-prismatic, tetragonal-prismatic, planar-square and hexagonal faceting 0.1 to 0.5 mm in size were obtained. The electronic transport and magnetic prop-erties measurements of FeSex single crystal exhibit an onset of superconducting transition Tc at up to 24 K.

cond-mat.supr-con↗