Laboratory of NumericaL methods of ppLied structuraL ... · State-of-the-art research in optimization theory and methods Goals Find elegant and simple solutions for complex actual

Laboratory of NumericaL

methods of

appLied

structuraL

optimizatioN

01.09.2018Laboratory NuMASO1

Mission &Goals


Mission Solving hard practical optimization problems State-of-the-art research in optimization theory and methods

Goals Find elegant and simple solutions for complex actual problems Create optimization method’s frameworks Extend the domain of optimization theory applicability Develop new numerical optimization methods and improve existing

ones Investigate optimization methods properties and effectiveness

Team. Lead Researchers

3

Dr. Mikhail PosypkinLead Researcher

Dr. Vitalii ZhadanLead Researcher

Dr. Alexandr GasnikovLead Researcher

Phd. Alexandr BiryukovSenior Researcher

Phd. Fedor StonyakinSenior Researcher

Dr. Vladimir ZubovLead Researcher

Phd. Andrey GorchakovSenior Researcher

Phd. Alexey ChernovSenior Researher – Deputy Head

Acad. Dr. Yury EvtushenkoChief Researcher – Head of the laboratory

Marina DanilovaJunior Researcher

Daniil MerkulovJunior Researcher

Dmitrii KamzolovJunior Researcher

01.09.2018Laboratory NuMASO

Laboratory Head Yury Evtushenko


Academic Degrees: 2006 Academician of the Russian

Academy of Sciences

1985 Professor

1981 Doctor of Physical and Mathematical Sciences, Computing Centre of the USSR Academy of Sciences (CCAS)

Research Interests: Linear and Nonlinear Programming

Decision Support Systems

Optimal Control

Optimization Techniques

Numerical Methods and Software for Solving Global MulticriteriaOptimization

Professional Experience: 1989 - p.t. Director of Dorodnicyn Computing

Centre of RAS 1981 - 1989 Deputy Director of Dorodnicyn

Computing Centre 1978 - 1981 Head of Subdepartment in the

Department of operation research, CCAS 1973 - 1978 Senior Researcher, CCAS 1967 - 1972 Junior Researcher, Computing Centre of

the USSR Academy of Sciences (CCAS) 1966 - 1967 Junior Researcher, Central

Aerohydrodynamic Institute (TsAGI) 1965 - 1966 Senior engineer (TsAGI) 1962 - 1965 Post graduate student at Moscow

Institute of Physics and Technology

Research Directions

Structural optimization Numerical methods of local and global optimization theory Multicriteria optimization Nonconvex and non-smooth optimization Linear and nonlinear programming, semidefinite and

equilibrium programming Numerical methods of optimal control Stochastic optimization High-performance techniques in optimization Distributed optimization


Competencies


Machine Learning Traffic assignment problems Computer networks modeling Inverse problems of mathematical physics Optimal Control in the Foundry Industry Global Optimization Robotics: Approximation of the Robot’s workspace Fast Automatic Differentiation Non-linear analysis and its applications Software Framework Software Development

Machine Learning

PageRank problem solution (nonconvex optimization)Cooperation with CORE UCL (Yu. Nesterov) Yandex

https://arxiv.org/pdf/1603.00717.pdf Distributed optimization with sum-type target functions

Cooperation with A. Nedichttps://arxiv.org/pdf/1712.00232.pdfhttps://arxiv.org/pdf/1803.02933.pdfhttps://arxiv.org/pdf/1806.03915.pdf

Image analysis (Monge-Kantorovich-Wasserstein transport distance)Cooperation with WIAS Berlin (P. Dvurechensky, V. Spokoiny)https://arxiv.org/pdf/1802.04367.pdf


https://arxiv.org/pdf/1603.00717.pdf





Traffic assignment problems Applications

Cars transport (http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=crm&paperid=256&option_lang=rus)

Railways (https://arxiv.org/ftp/arxiv/papers/1501/1501.02205.pdf)

Short-term modeling and Long-term modeling: traffic assignment problems, mechanism design (road pricing) How to predict the situation on the roads for an hour

ahead? How to road price to achieve a system optimum? Where is it necessary to make reverse strips and dedicated

lanes for public transport? How to optimally manage traffic signaling and access to

major highways? How to optimally manage traffic flows?

Publics: Edited by Gasnikov A.V. Introduction in mathematical

modeling traffic flows // MCCME – Moscow, 2013.


http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=crm&paperid=256&option_lang=rus

https://arxiv.org/ftp/arxiv/papers/1501/1501.02205.pdf

Computer networks modeling & inverse problems of mathematical physics

Inverse problems of mathematical physicshttps://arxiv.org/ftp/arxiv/papers/1703/1703.00267.pdfCooperation with A. Kabanikhin (Novosibirsk)

Modeling of computer networks (Large scale and huge scale optimizationhttps://arxiv.org/ftp/arxiv/papers/1508/1508.00858.pdfCooperation with




Optimal Control in the Foundry Industry


Control of the process of crystallization of metal in the foundry industryA.V. Albu, A.F. Albu, V.I. Zubov. Mathematical modeling and control of the process of crystallization of metal in the foundry business. Scientific publication. Computing Center. A.A. Dorodnitsyn of the Russian Academy of Sciences. Moscow. 2012. 168 C.

Optimal control for foundry formu(t) is the velocity of the foundry form

Optimal Control in the Foundry Industry


Determination of the thermal conductivity of a substance by the dynamics of the temperature fieldA. Albu, V. Zubov. Identification of the thermal conductivity coefficient in two dimension case // Optim Lett (2018). https://doi.org/10.1007/s11590-018-1304-4 V. Zubov. Application of the methodology of rapid automatic differentiation to the solution of the inverse coefficient problem for the heat equation // Zh. Vychisl. Math. and Math. fiz. 2016. P. 56. № 10. P. 1760-1774.

"Recovery" of the function K (T) over a given temperature field with machine quality (accuracy)2100196.3 −⋅=iniФ 26109909.2 −⋅=optФ

Global Optimization

Overview

Publications


A deterministic global optimization method Allows to approximate function extrema, sets given by the system of equations, inequalities

or mapping with the pre-defined precision Method was successfully parallelized for multicore systems with shared and distributed

memory organization

1. Evtushenko Y. G. Computation of exact gradients in distributed dynamic systems // Optimization Methods and Software. – 1998. – V. 9. – P. 45-75

2. Evtushenko Y. G. Numerical methods for finding global extrema (case of a non-uniform mesh) //Computational Mathematics and Mathematical Physics. – 1971. – V. 11. – No. 6. – P. 38-54.

3. Evtushenko Y., Posypkin M. A deterministic approach to global box-constrained optimization //Optimization Letters. – 2013. – V. 7. – No. 4. – P. 819-829.

4. Evtushenko Y. G., Posypkin M. A. A deterministic algorithm for global multi-objective optimization //Optimization Methods and Software. – 2014. – V. 29. – No. 5. – P. 1005-1019.

5. Evtushenko Y., Posypkin M., Sigal I. A framework for parallel large-scale global optimization //Computer Science-Research and Development. – 2009. – V. 23. – No. 3-4. – P. 211-215.

6. Evtushenko, Y., Golubeva, Y., Orlov, Y., Posypkin, M.Using simulation for performance analysis and visualization of parallel Branch-and-Bound methods //Russian Supercomputing Days. – Springer, Cham, 2016. – P. 356-368.

7. Evtushenko Y. G., Posypkin M. A. Effective hull of a set and its approximation //Doklady Mathematics. –Pleiades Publishing, 2014. – V. 90. – No. 3. – P. 791-794.

8. Evtushenko, Y., Posypkin, M., Rybak, L., Turkin, A.. Approximating a solution set of nonlinear inequalities //Journal of Global Optimization. – 2017. – P. 1-17.

Robotics: Approximation of the Robot’s workspace

DexTAR parallel robot Workspace


Robotics: Approximation of the Robot’s workspace

The scientific reserve in the field of modeling of robotsof parallel structure is created.

Methods for approximating the working area of therobot and the corresponding software have beendeveloped.

Approaches have been developed for solving robotcontrol problems, based on the methodology of rapidautomatic differentiation of objective functions and taskconstraints.


Fast Automatic Differentiation

FAD technique: development of high-performance packages4D-Var data assimilations

Initial conditions search

spherical wave


Non-linear analysis and its applications


Applications of non-linear analysis inextremal problems (analogues of Ferma-Torrichelli-Shteiner problem)http://www.apmath.spbu.ru/cnsa/pdf/monograf/Выпуклый%20и%20негладкий%20анализ%20Орлов%20Стонякин%20Смирнова.pdf

Universal and adaptive methods for variationinequities and saddle problems. Equilibriumsearch problemshttps://arxiv.org/abs/1804.02579https://arxiv.org/abs/1806.05140

Optimization of functional with non-standard growth conditions, incl. arisingwhen solving problems Truss TopologyDesign.https://arxiv.org/abs/1710.06612https://arxiv.org/abs/1803.01329

http://www.apmath.spbu.ru/cnsa/pdf/monograf/%D0%92%D1%8B%D0%BF%D1%83%D0%BA%D0%BB%D1%8B%D0%B9%20%D0%B8%20%D0%BD%D0%B5%D0%B3%D0%BB%D0%B0%D0%B4%D0%BA%D0%B8%D0%B9%20%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%20%D0%9E%D1%80%D0%BB%D0%BE%D0%B2%20%D0%A1%D1%82%D0%BE%D0%BD%D1%8F%D0%BA%D0%B8%D0%BD%20%D0%A1%D0%BC%D0%B8%D1%80%D0%BD%D0%BE%D0%B2%D0%B0.pdf

https://arxiv.org/abs/1804.02579




Software framework


NUMERIC UTILITIES

INTERVAL ARITHMETICS

LIBRARY

EXPRESSIONS LIBRARY

NON-UNIFORM COVERING

METHOD “LOGIC”

SEQUENTIAL

SHARED MEMORY

DISTRIBUTED MEMORY

GPU (CUDA)

DISTRBUTED (BOINC)

Software framework: Expressions library


• Allows to declare complex formulas

• Supports automated evaluation of a function value, its derivatives, interval bounds and interval bounds for derivatives

template <classT> Expr<T> Rosenbrock(int n) {Expr<T> x;Iterator i(0, n-2);Expr<T> t = i;return loopSum(100*sqr(x[t+1]-sqr(x[i]))+sqr((x[i]-1)), i);

}

Software Development

Iterative and incremental Waterfall


Project Development

Life cycles

Starting the project

Organizing and Preparing

Carrying out the project

work

Closing the project



Project Documentation

Version control systems



Hadoop Technology stack

Programming Languages & Frameworks

Databases

Platforms

IDEs

Documents

Laboratory of NumericaL methods of ppLied structuraL ... · State-of-the-art research in optimization theory and methods Goals Find elegant and simple solutions for complex actual