arXiv subjects

Alexander Titov

Publications and source records attributed to Alexander Titov.

14 recordsLinked to original sources

arXiv2023

Formation of spiral dwarf galaxies: observational data and results of numerical simulation

Recent studies show the possibility of the formation of fairly regular and global spiral patterns in dwarf galaxies (dS type). Our sample of observed dwarf objects of this class also includes galaxies with a central stellar bar. The analysis of the observational data provides a small rotation velocity and a small disk component mass for dS galaxies, which is in poor agreement with the spiral structure generation mechanism in isolated dwarfs due to the development of disk gravitational instability. Numerical simulation of the stellar-gaseous disks self-consistent dynamics imposes restrictions on the stellar disk thickness and the maximum gas rotation velocity, at which the gravitational mechanism of spiral formation can still be effective.

astro-ph.GA↗

arXiv2023

Online Optimization Problems with Functional Constraints under Relative Lipschitz Continuity and Relative Strong Convexity Conditions

Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significantly expanded the class of problems for which optimal complexity estimates of gradient-type methods in high-dimensional spaces take place. Basing on some recent works devoted to online optimization (regret minimization) problems with both relatively Lipschitz continuous and relatively strongly convex objective function, we introduce algorithms for solving the strongly convex optimization problem with inequality constraints in the online setting. We propose a scheme with switching between productive and nonproductive steps for such types of problems and prove its convergence rate for the class of relatively Lipschitz and strongly convex minimization problems. We also provide an experimental comparison between the proposed method and AdaMirr, recently proposed for relatively Lipschitz convex problems.

math.OC↗

arXiv2022

Optimization in complex spaces with the Mixed Newton Method

We propose a second-order method for unconditional minimization of functions $f(z)$ of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger derivative $\frac{\partial^2f}{\partial\bar z\partial z}$ for computation of the search direction, as opposed to the full Hessian $\frac{\partial^2f}{\partial(z,\bar z)^2}$ in the classical Newton method. The method has been developed for specific applications in wireless network communications, but its global convergence properties are shown to be superior on a more general class of functions $f$, namely sums of squares of absolute values of holomorphic functions. In particular, for such objective functions minima are surrounded by attraction basins, while the iterates are repelled from other types of critical points. We provide formulas for the asymptotic convergence rate and show that in the scalar case the method reduces to the well-known complex Newton method for the search of zeros of holomorphic functions. In this case, it exhibits generically fractal global convergence patterns.

math.OC↗

arXiv2021

Mirror Descent and Constrained Online Optimization Problems

We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The problem is to minimize the arithmetic mean of functionals with a convex Lipschitz-continuous non-smooth constraint. In addition, it is allowed to calculate the (sub)gradient of each functional only once. Using some recently proposed adaptive methods of Mirror Descent the method is suggested to solve the mentioned constrained online optimization problem with optimal estimate of accuracy. For the corresponding non-Euclidean prox-structure the case of a set of $n$-dimensional vectors lying on the standard $n$-dimensional simplex is considered.

math.OC↗

arXiv2021

Mirror Descent for Constrained Optimization Problems with Large Subgradient Values

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some novel strategies of step-sizes and adaptive stopping rules in Mirror Descent algorithms for the considered class of problems. It is shown that the methods are applicable to the objective functionals of various levels of smoothness. Applying the restart technique to the Mirror Descent Algorithm there was proposed an optimal method to solve optimization problems with strongly convex objective functionals. Estimates of the rate of convergence of the considered algorithms are obtained depending on the level of smoothness of the objective functional. These estimates indicate the optimality of considered methods from the point of view of the theory of lower oracle bounds. In addition, the case of a quasi-convex objective functional and constraint was considered.

math.OC↗

arXiv2021

Conceptual Design Report for the LUXE Experiment

This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) effective field strengths to be probed at and beyond the Schwinger limit and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout.

hep-ex↗

arXiv2021

Adaptive Algorithms for Relatively Lipschitz Continuous Convex Optimization Problems

Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods with optimal estimates of the convergence rate, which are invariant regardless of the dimensionality of the problem. Later Yu. Nesterov and H. Lu introduced some modifications of the Mirror Descent method for convex minimization problems with the corresponding analogue of the Lipschitz condition (so-called relative Lipschitz continuity). By introducing an artificial inaccuracy to the optimization model, we propose adaptive methods for minimizing a convex Lipschitz continuous function, as well as for the corresponding class of variational inequalities. We also consider an adaptive "universal" method, applicable to convex minimization problems both on the class of relatively smooth and relatively Lipschitz continuous functionals with optimal estimates of the convergence rate. The universality of the method makes it possible to justify the applicability of the obtained theoretical results to a wider class of convex optimization problems. We also present the results of numerical experiments.

math.OC↗

arXiv2021

Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems

Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective function and functional constraints. We introduce a new concept of an inexact model and propose some analogues of switching subgradient schemes for convex programming problems for the relatively Lipschitz-continuous objective function and functional constraints. Some class of online convex optimization problems is considered. The proposed methods are optimal in the class of optimization problems with relatively Lipschitz-continuous objective and functional constraints.

math.OC↗

arXiv2021

Algorithms for solving variational inequalities and saddle point problems with some generalizations of Lipschitz property for operators

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some notable methods for optimization problems with strongly monotone operators. Our focus here is on newly proposed techniques for solving strongly convex-concave saddle point problems. One of the goals of the article is to improve the obtained estimates of the complexity of introduced algorithms by using accelerated methods for solving auxiliary problems. The second focus of the article is introducing an analogue of the boundedness condition for the operator in the case of arbitrary (not necessarily Euclidean) prox structure. We propose an analogue of the mirror descent method for solving variational inequalities with such operators, which is optimal in the considered class of problems.

math.OC↗

arXiv2020

Comparative analysis of $ωp$, $ϕp$, and $J/ψp$ scattering lengths from A2, CLAS, and GlueX threshold measurements

The high accuracy $ϕ$-meson photoproduction data from the CLAS experiment in Hall~B of Jefferson Laboratory allow us to determine the near-threshold total cross section of the $γp\toϕp$ reaction and use it for evaluating the $ϕp$ scattering length $α_{ϕp}$. These data result in an absolute value of $|α_{ϕp}| = (0.063\pm 0.010)$~fm, which is smaller than the typical hadron size. A comparative analysis of $α_{ϕp}$ with the previously determined scattering lengths for $ωp$ and $J/ψp$ from the A2 and GlueX experiments is performed.

hep-ph↗

arXiv2018

Adaptive Proximal Method for Variational Inequalities

A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A generalization of the method under consideration to the case of a Holder-continuous field is considered.

math.OC↗

arXiv2018

Generalized Mirror Prox for Monotone Variational Inequalities: Universality and Inexact Oracle

We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. As a particular case, we consider VI's with H\"older-continuous operator and show that our algorithm is universal. This means that without knowing the H\"older parameter $\nu$ and H\"older constant $L_{\nu}$ it has the best possible complexity for this class of VI's, namely our algorithm has complexity $O\left( \inf_{\nu\in[0,1]}\left(\frac{L_{\nu}}{\varepsilon} \right)^{\frac{2}{1+\nu}}R^2 \right)$, where $R$ is the size of the feasible set and $\varepsilon$ is the desired accuracy of the solution. We also consider the case of VI's with strongly monotone operator and generalize our method for VI's with inexact oracle and our universal method for this class of problems. Finally, we show, how our method can be applied to convex-concave saddle point problems with H\"older-continuous partial subgradients.

math.OC↗

arXiv2018

Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint. We hope that it is convenient for a reader to have all the methods for different settings in one place. Described methods are based on Mirror Descent algorithm and switching subgradient scheme. One of our focus is to propose, for the listed different settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule. This means that neither stepsize nor stopping rule require to know the Lipschitz constant of the objective or constraint. We also construct Mirror Descent for problems with objective function, which is not Lipschitz continuous, e.g. is a quadratic function. Besides that, we address the problem of recovering the solution of the dual problem.

math.OC↗

arXiv2013

$ϕN$ photoproduction coupled with the $KΛ^*$ channel

We present in this talk a recent investigation on $ϕ$ photoproduction, emphasizing the rescattering effects of the $KΛ^*$ channel near the threshold region. We discuss the results of the differential cross section and the angular distributions.

hep-ph↗