Direct-dual method of mirror descent for conditional problems of stochastic optimization

 
PIIS004446690003533-7-1
DOI10.31857/S004446690003533-7
Publication type Article
Status Published
Authors
Affiliation: Faculty of Management and Applied Mathematics of the National Research University "Moscow Institute of Physics and Technology"
Address: Russian Federation
Affiliation:
Department of Mathematical Foundations of Management of the National Research University "Moscow Institute of Physics and Technology"
36 / 10000 АНГЛИЙСКИЙ Перевести вGoogleBing Institute of information transmission problems, RAS
Address: Russian Federation
Affiliation: Moscow Institute of Physics and Technology
Address: Russian Federation, Moscow region, Dolgoprudny
Affiliation: Baltic Federal University. I. Kant
Address: Russian Federation, Kaliningrad
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 11
Pages1794-1803
Abstract

  

Keywords
Received15.01.2019
Publication date15.01.2019
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1. Nemirovskij A.S., Yudin D. B. Slozhnost' zadach i ehffektivnost' metodov optimizatsii. M.: Nauka, 1979.

2. Anikin A.S., Gasnikov A. V., Gornov A. Yu. R andomizatsiya i razrezhennost' v zadachakh huge-scale optimizatsii na primere raboty metoda zerkal'nogo spuska // Trudy MFTI. 2016. T. 8. № 1. S. 11–24. arXiv:1602.00594

3. Kim K., Nesterov Yu., Skokov V., Cherkasskij B. Ehffektivnye algoritmy dlya differentsirovaniya i zadachi ehkstremali // Ehkonomika i matematicheskie metody.– 1984. – T . 20. – S. 309–318.

4. Nesterov Yu. Lexicographic differentiation of nonsmooth functions // Math. Prog.– 2005. – V. 104. – no. 2–3. – P. 669–700.

5. Gasnikov A.V., Dvurechenskij P. E., Dorn Yu. V., Maksimov Yu. V. Chislennye metody poiska ravnovesnogo raspredeleniya potokov v modeli Behkmana i modeli stabil'noj dinamiki // Matematicheskoe modelirovanie. 2016. T. 28. № 10. S. 40–64. arXiv:1506.00293

6. Juditsky A., Lan G., Nemirovski A., Shapiro A. Stochastic approximation approach to stochastic programming // SIAM Journal on Optimization. 2009. V. 19. № 4. P. 1574–1609.

7. Boucheron S., Lugoshi G., Massart P. Concentration inequalities: A nonasymptotic theory of independence. Oxford University Press, 2013.

8. Nesterov Yu., Shpirko S. Primal-dual subgradient method for huge-scale linear conic problem // SIAM Journal on Optimization. 2014. V. 24. № . 3. P. 1444–1457. http://www.optimization-online.org/DB_FILE/2012/08/3590.pdf

9. Nesterov Yu. New primal-dual subgradient methods for convex optimization problems with functional constraints // International Workshop “Optimization and Statistical Learning”. January 11–16. France, Les Houches, 2015. http://lear.inrialpes.fr/workshop/osl2015/program.html

10. Anikin A.S., Gasnikov A. V., Dvurechenskij P. E., Tyurin A. I., Chernov A. V. Dvojstvennye podkhody k zadacham minimizatsii sil'no vypuklykh funktsionalov prostoj struktury pri affinnykh ogranicheniyakh // ZhVM i MF. 2017. T. 57. № 6. (v pechati) arXiv:1602.01686

11. Nemirovski A., Onn S., Rothblum U. G. Accuracy certificates for computational problems with convex structure // Mathematics of Operation Research. 2010. V. 35. № 1. P. 52–78.

12. Cox B., Juditsky A., Nemirovski A. Decomposition techniques for bilinear saddle point problems and variational inequalities with affine monotone operators on domains given by linear minimization oracles // e-print, 2015. arXiv:1506.02444

13. Juditsky A., Nemirovski A. First order methods for nonsmooth convex large-scale optimization, I, II. // Optimization for Machine Learning. // Eds. S. Sra, S. Nowozin, S. Wright. – MIT Press, 2012.

14. Gasnikov A.V., Krymova E. A., Lagunovskaya A. A., Usmanova I. N., Fedorenko F. A. Stokhasticheskaya onlajn optimizatsiya. Odnotochechnye i dvukhtochechnye nelinejnye mnogorukie bandity. Vypuklyj i sil'no vypuklyj sluchai // Avtomatika i telemekhanika. 2017. (v pechati) arXiv:1509.01679

15. Duchi J. C. Introductory Lectures on Stochastic Optimization // IAS/Park City Mathematics Series. 2016. P. 1–84. http://stanford.edu/~jduchi/PCMIConvex/Duchi16.pdf

16. Nesterov Yu. Subgradient methods for convex function with nonstandart growth properties // e-print, 2016. http://www.mathnet.ru:8080/PresentFiles/16179/growthbm_nesterov.pdf

17. Duchi J.C., Shalev-Shwartz S., Singer Y., Tewari A. Composite objective mirror descent // Proceedings of COLT.– 2010. – P. 14–26.

18. Juditsky A., Nesterov Yu. Deterministic and stochastic primal-dual subgradient algorithms for uniformly convex minimization // Stoch. System.– 2014. – V. 4. – no. 1. – P. 44–80.

19. Anikin A.S., Gasnikov A. V., Gornov A. Yu., Kamzolov D. I., Maksimov Yu. V., Nesterov Yu. E. Ehffektivnye chislennye metody resheniya zadachi PageRank dlya dvazhdy razrezhennykh matrits // Trudy MFTI. 2015. T. 7. № 4. S. 74–94. arXiv:1508.07607

20. https://github.com/anastasiabayandina/Mirror

21. Beck A., Ben-Tal A., Guttmann-Beck N., Tetruashvili L. The CoMirror algorithm for solving nonsmooth constrained convex problems // Operations Research Letters.– 2011. V. 38. No. 6. P. 493–498.

22. Juditsky A., Nemirovski A., Tauvel C. Solving variational inequalities with Stochastic Mirror-Prox algorithm // Stochastic Systems.– 2011. V. 1. no. 1. P. 17–58.

23. Lan G., Zhou Z. Algorithms for stochastic optimization with expectation constraints // e-print, 2016.

24. http://pwp.gatech.edu/guanghui-lan/wp-content/uploads/sites/330/2016/08/SPCS8–19–16.pdf

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