Stonyakin, Fedor; Kuruzov, Ilya; Polyak, Boris Stopping rules for gradient methods for non-convex problems with additive noise in gradient. (English) Zbl 1522.90141 J. Optim. Theory Appl. 198, No. 2, 531-551 (2023). MSC: 90C26 90C52 65K05 PDFBibTeX XMLCite \textit{F. Stonyakin} et al., J. Optim. Theory Appl. 198, No. 2, 531--551 (2023; Zbl 1522.90141) Full Text: DOI arXiv
Fatkhullin, Ilyas; Polyak, Boris Optimizing static linear feedback: gradient method. (English) Zbl 1475.49039 SIAM J. Control Optim. 59, No. 5, 3887-3911 (2021). MSC: 49N10 49N35 49M37 90C26 90C52 PDFBibTeX XMLCite \textit{I. Fatkhullin} and \textit{B. Polyak}, SIAM J. Control Optim. 59, No. 5, 3887--3911 (2021; Zbl 1475.49039) Full Text: DOI arXiv
Polyak, B. T.; Fatkhullin, I. F. Use of projective coordinate descent in the Fekete problem. (English. Russian original) Zbl 1453.90166 Comput. Math. Math. Phys. 60, No. 5, 795-807 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 5, 815-827 (2020). MSC: 90C30 90C90 PDFBibTeX XMLCite \textit{B. T. Polyak} and \textit{I. F. Fatkhullin}, Comput. Math. Math. Phys. 60, No. 5, 795--807 (2020; Zbl 1453.90166); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 5, 815--827 (2020) Full Text: DOI
Polyak, Boris T.; Kvinto, Yana I. Stability and synchronization of oscillators: new Lyapunov functions. (English. Russian original) Zbl 1373.93250 Autom. Remote Control 78, No. 7, 1234-1242 (2017); translation from Avtom. Telemekh. 2017, No. 7, 76-85 (2017). MSC: 93D05 93D30 93C15 93C10 70Q05 PDFBibTeX XMLCite \textit{B. T. Polyak} and \textit{Y. I. Kvinto}, Autom. Remote Control 78, No. 7, 1234--1242 (2017; Zbl 1373.93250); translation from Avtom. Telemekh. 2017, No. 7, 76--85 (2017) Full Text: DOI
Boyaryshcheva, T. V.; Polyak, I. J. Estimate of closeness of densities of distributions of two sums of random variables. (Ukrainian. English summary) Zbl 1245.62032 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 22, 35-38 (2011). MSC: 62G07 PDFBibTeX XMLCite \textit{T. V. Boyaryshcheva} and \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 22, 35--38 (2011; Zbl 1245.62032)
Griva, Igor; Polyak, Roman A. Proximal point nonlinear rescaling method for convex optimization. (English) Zbl 1268.90046 Numer. Algebra Control Optim. 1, No. 2, 283-299 (2011). MSC: 90C25 90C30 PDFBibTeX XMLCite \textit{I. Griva} and \textit{R. A. Polyak}, Numer. Algebra Control Optim. 1, No. 2, 283--299 (2011; Zbl 1268.90046) Full Text: DOI
Boyaryshcheva, T. V.; Polyak, I. J.; Slyusarchuk, P. V. An estimate of the rate of convergence of the distribution function of a two-dimensional random vector to the distribution function of a two-dimensional normal law. (Ukrainian. English summary) Zbl 1199.60073 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 18, 31-38 (2009). MSC: 60F15 PDFBibTeX XMLCite \textit{T. V. Boyaryshcheva} et al., Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 18, 31--38 (2009; Zbl 1199.60073)
Boyaryshcheva, T. V.; Polyak, I. J. The rate of convergence to a two-dimensional normal law in the uniform metric for characteristic functions. (Ukrainian. English summary) Zbl 1199.60072 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 18, 25-30 (2009). MSC: 60F15 PDFBibTeX XMLCite \textit{T. V. Boyaryshcheva} and \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 18, 25--30 (2009; Zbl 1199.60072)
Boyaryshscheva, T. V.; Polyak, I. J.; Slyusarchuk, P. V. Estimates of the rate of convergence in local limit theorem for densities. (Ukrainian. English summary) Zbl 1164.60325 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 16, 35-39 (2008). MSC: 60F05 PDFBibTeX XMLCite \textit{T. V. Boyaryshscheva} et al., Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 16, 35--39 (2008; Zbl 1164.60325)
Griva, Igor; Polyak, Roman A. 1.5-\(Q\)-superlinear convergence of an exterior-point method for constrained optimization. (English) Zbl 1149.90146 J. Glob. Optim. 40, No. 4, 679-695 (2008). Reviewer: Jörg Thierfelder (Ilmenau) MSC: 90C30 49M37 65K05 PDFBibTeX XMLCite \textit{I. Griva} and \textit{R. A. Polyak}, J. Glob. Optim. 40, No. 4, 679--695 (2008; Zbl 1149.90146) Full Text: DOI
Polyak, Roman; Ho, Shen-Shyang; Griva, Igor Support vector machine via nonlinear rescaling method. (English) Zbl 1220.90079 Optim. Lett. 1, No. 4, 367-378 (2007). MSC: 90C20 90C46 90C25 PDFBibTeX XMLCite \textit{R. Polyak} et al., Optim. Lett. 1, No. 4, 367--378 (2007; Zbl 1220.90079) Full Text: DOI
Mordvitsev, D. Yu.; Polyak, Ya. L.; Kuzmin, D. A.; Levtsova, O. V.; Tourleigh, Ye. V.; Utkin, Yu. N.; Shaitan, K. V.; Tsetlin, V. I. Computer modeling of binding of diverse weak toxins to nicotinic acetylcholine receptors. (English) Zbl 1124.92017 Comput. Biol. Chem. 31, No. 2, 72-81 (2007). MSC: 92C40 PDFBibTeX XMLCite \textit{D. Yu. Mordvitsev} et al., Comput. Biol. Chem. 31, No. 2, 72--81 (2007; Zbl 1124.92017) Full Text: DOI
Polyak, I. J. Refinement of the local limit theorem in the series scheme. (Ukrainian. English summary) Zbl 1118.60304 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 12-13, 99-102 (2006). MSC: 60F05 PDFBibTeX XMLCite \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 12--13, 99--102 (2006; Zbl 1118.60304)
Griva, Igor; Polyak, Roman A. Primal-dual nonlinear rescaling method with dynamic scaling parameter update. (English) Zbl 1134.90494 Math. Program. 106, No. 2 (A), 237-259 (2006). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{I. Griva} and \textit{R. A. Polyak}, Math. Program. 106, No. 2 (A), 237--259 (2006; Zbl 1134.90494) Full Text: DOI
Boyaryshcheva, T. V.; Polyak, I. J.; Slyusarchuk, P. V. On the rate of convergence to the normal law. (Ukrainian. English summary) Zbl 1118.60303 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 10-11, 34-40 (2005). MSC: 60F05 PDFBibTeX XMLCite \textit{T. V. Boyaryshcheva} et al., Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 10--11, 34--40 (2005; Zbl 1118.60303)
Mordvintsev, D. Yu.; Polyak, Ya. L.; Levtsova, O. V.; Tourleight, Ye. V.; Kasheverov, I. E.; Shaitan, K. V.; Utkin, Yu. N.; Tsetlin, V. I. A model for short \(\alpha\)-neurotoxin bound to nicotinic acetylcholine receptor from Torpedo californica: Comparison with long-chain \(\alpha\)-neurotoxins and \(\alpha\)-conotoxins. (English) Zbl 1108.92301 Comput. Biol. Chem. 29, No. 6, 398-411 (2005). MSC: 92C40 92C50 PDFBibTeX XMLCite \textit{D. Yu. Mordvintsev} et al., Comput. Biol. Chem. 29, No. 6, 398--411 (2005; Zbl 1108.92301) Full Text: DOI
Chernousko, Felix (ed.); Polyak, Boris (ed.) Special issue: Set-membership modeling of uncertainties in dynamical systems. Papers based on the presentation at the 3rd and 4th IMACS symposia on mathematical modeling, Vienna, Austria, February 2–4, 2000, and February 5–7, 2003. (English) Zbl 1080.93502 Math. Comput. Model. Dyn. Syst. 11, No. 2, 123-249 (2005). MSC: 93-06 00B25 PDFBibTeX XMLCite \textit{F. Chernousko} (ed.) and \textit{B. Polyak} (ed.), Math. Comput. Model. Dyn. Syst. 11, No. 2, 123--249 (2005; Zbl 1080.93502) Full Text: DOI
Polyak, R.; Griva, I. Primal-dual nonlinear rescaling method for convex optimization. (English) Zbl 1129.90339 J. Optim. Theory Appl. 122, No. 1, 111-156 (2004). MSC: 90C25 90C46 90C51 PDFBibTeX XMLCite \textit{R. Polyak} and \textit{I. Griva}, J. Optim. Theory Appl. 122, No. 1, 111--156 (2004; Zbl 1129.90339) Full Text: DOI
Polyak, I. J. Some estimate of the rate of convergence to the normal law. (Ukrainian, English) Zbl 1050.60027 Teor. Jmovirn. Mat. Stat. 68, 112-114 (2003); translation in Theory Probab. Math. Stat. 68, 123-126 (2004). Reviewer: A. D. Borisenko (Kyïv) MSC: 60F10 PDFBibTeX XMLCite \textit{I. J. Polyak}, Teor. Ĭmovirn. Mat. Stat. 68, 112--114 (2003; Zbl 1050.60027); translation in Theory Probab. Math. Stat. 68, 123--126 (2004)
Polyak, Ivan J. Estimation of closeness of densities of distributions of two sums. (Ukrainian. English summary) Zbl 1030.62031 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2002, No. 4, 27-30 (2002). MSC: 62G07 62G20 60E07 PDFBibTeX XMLCite \textit{I. J. Polyak}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2002, No. 4, 27--30 (2002; Zbl 1030.62031)
Polyak, Roman A.; Griva, Igor; Sobieszczanski-Sobieski, Jarek Nonlinear rescaling in discrete minimax. (English) Zbl 0983.74054 Gao, David Y. (ed.) et al., Nonsmooth/ nonconvex mechanics. Modeling, analysis and numerical methods. A volume dedicated to the memory of Prof. P. D. Panagiotopoulos. Minisymposium within the ASME 1999 Mechanics and materials conference, Blacksburg, VA, USA, June 27-30, 1999. Boston: Kluwer Academic Publishers. Nonconvex Optim. Appl. 50, 301-331 (2001). MSC: 74P99 65K10 PDFBibTeX XMLCite \textit{R. A. Polyak} et al., Nonconvex Optim. Appl. 50, 301--331 (2001; Zbl 0983.74054)
Boyaryshcheva, T. V.; Polyak, I. J.; Slyusarchuk, P. V. Estimate of closeness of distributions of sums to normal distribution. (Ukrainian. English summary) Zbl 0981.60016 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 5, 4-10 (2000). Reviewer: A.D.Borisenko (Kyïv) MSC: 60F05 PDFBibTeX XMLCite \textit{T. V. Boyaryshcheva} et al., Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 5, 4--10 (2000; Zbl 0981.60016)
Goldfarb, D.; Polyak, R.; Scheinberg, K.; Yuzefovich, I. A modified barrier-augmented Lagrangian method for constrained minimization. (English) Zbl 0951.90042 Comput. Optim. Appl. 14, No. 1, 55-74 (1999). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{D. Goldfarb} et al., Comput. Optim. Appl. 14, No. 1, 55--74 (1999; Zbl 0951.90042) Full Text: DOI
Slyusarchuk, P. V.; Polyak, I. J. Generalization of some V. M. Zolotarev’s result. (Ukrainian. English summary) Zbl 0973.60023 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 3, 184-189 (1998). Reviewer: A.D.Borisenko (Kyïv) MSC: 60F05 PDFBibTeX XMLCite \textit{P. V. Slyusarchuk} and \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 3, 184--189 (1998; Zbl 0973.60023)
Polyak, I. J. Some nonuniform estimate in the central limit theorem. (Ukrainian. English summary) Zbl 0973.60024 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 3, 169-170 (1998). Reviewer: A.D.Borisenko (Kyïv) MSC: 60F05 PDFBibTeX XMLCite \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 3, 169--170 (1998; Zbl 0973.60024)
Slyusarchuk, P. V.; Polyak, I. J. Some estimates of the rate of convergence in the central limit theorem. (Ukrainian) Zbl 0942.60013 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 2, 104-107 (1997). MSC: 60F05 PDFBibTeX XMLCite \textit{P. V. Slyusarchuk} and \textit{I. J. Polyak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 2, 104--107 (1997; Zbl 0942.60013)
Polyak, Ilya Computational statistics in climatology. (English) Zbl 0905.62124 New York, NY: Oxford University Press. xiii, 358 p. (1996). Reviewer: V.P.Gupta (Jaipur) MSC: 62P99 86A10 62H11 62-02 62M10 PDFBibTeX XMLCite \textit{I. Polyak}, Computational statistics in climatology. New York, NY: Oxford University Press (1996; Zbl 0905.62124)
Tsypkin, Ya. Z.; Polyak, B. T.; Katbab, A.; Jury, E. I. On the strict- and wide-sense stability robustness of uncertain systems: Application of a new frequency criterion. (English) Zbl 0818.93052 Syst. Control Lett. 22, No. 5, 377-383 (1994). Reviewer: M.Z.Nashed (Newark / Delaware) MSC: 93D09 93B51 93C05 PDFBibTeX XMLCite \textit{Ya. Z. Tsypkin} et al., Syst. Control Lett. 22, No. 5, 377--383 (1994; Zbl 0818.93052) Full Text: DOI
Gudivok, P. M.; Kapitonova, Yu. V.; Polyak, S. S.; Rud’ko, V. P.; Tsitkin, A. I. Classes of conjugate elements of the unitriangular group. (English. Russian original) Zbl 0761.20022 Cybernetics 26, No. 1, 47-57 (1990); translation from Kibernetika 1990, No. 1, 40-48 (1990). MSC: 20G35 15A30 PDFBibTeX XMLCite \textit{P. M. Gudivok} et al., Cybernetics 26, No. 1, 47--57 (1990; Zbl 0761.20022); translation from Kibernetika 1990, No. 1, 40--48 (1990)
Zuhovickii, S. I.; Poljak, R. A.; Primak, M. E. On a general problem of determining equilibrium. (English. Russian original) Zbl 0297.90090 Sov. Math., Dokl. 14, 368-372 (1973); translation from Dokl. Akad. Nauk SSSR 209, 279-282 (1973). MSC: 90C30 PDFBibTeX XMLCite \textit{S. I. Zuhovickii} et al., Sov. Math., Dokl. 14, 368--372 (1973; Zbl 0297.90090); translation from Dokl. Akad. Nauk SSSR 209, 279--282 (1973)
Zuhovickii, S. I.; Poljak, R. A.; Primak, M. E. Das Gleichgewichtsproblem und Methoden seiner Lösung. (Russian) Zbl 0246.90003 Wiss. Z. Hochschule Architektur Bauwesen Weimar 19, 224-226 (1972). MSC: 91B60 90C90 74K99 PDFBibTeX XMLCite \textit{S. I. Zuhovickii} et al., Wiss. Z. Hochsch. Archit. Bauwes. Weimar 19, 224--226 (1972; Zbl 0246.90003)
Zukhovitskiĭ, S. I.; Polyak, R. A.; Primak, M. E. On an \(n\)-person concave game and a production model. (English. Russian original) Zbl 0213.46501 Sov. Math., Dokl. 11, 522-526 (1970); translation from Dokl. Akad. Nauk SSSR 191, 1220-1223 (1970). MSC: 91A06 90B30 PDFBibTeX XMLCite \textit{S. I. Zukhovitskiĭ} et al., Sov. Math., Dokl. 11, 522--526 (1970; Zbl 0213.46501); translation from Dokl. Akad. Nauk SSSR 191, 1220--1223 (1970)
Zukhovitskij, S. I.; Polyak, R. A.; Primak, M. E. An algorithm to construct the Chebyshev net of a finite system of points. (Russian) Zbl 0225.65013 Wiss. Z. Hochschule Architektur Bauwesen Weimar 16, 299-301 (1969); V. Internationaler Kongress über Anwendungen der Mathematik in den Ingenieurwissenschaften. MSC: 65D05 PDFBibTeX XMLCite \textit{S. I. Zukhovitskij} et al., Wiss. Z. Hochsch. Archit. Bauwes. Weimar 16, 299--301 (1969; Zbl 0225.65013)
Zukhovitskiĭ, S. I.; Polyak, R. A.; Primak, M. E. Two methods of search for equilibrium points of \(n\)-person concave games. (English. Russian original) Zbl 0191.49801 Sov. Math., Dokl. 10, 279-282 (1969); translation from Dokl. Akad. Nauk SSSR 185, 24-27 (1969). Reviewer: Ezio Marchi MSC: 91A06 PDFBibTeX XMLCite \textit{S. I. Zukhovitskiĭ} et al., Sov. Math., Dokl. 10, 279--282 (1969; Zbl 0191.49801); translation from Dokl. Akad. Nauk SSSR 185, 24--27 (1969)
Zukhovitskiĭ, S. I.; Polyak, R. A.; Primak, M. E. A problem of nonconvex programming. (English. Russian original) Zbl 0208.22002 Sov. Phys., Dokl. 13, 296-298 (1968); translation from Dokl. Akad. Nauk SSSR 179, 786-789 (1968). Reviewer: S. L. Mehndiratta MSC: 90C26 90C35 PDFBibTeX XMLCite \textit{S. I. Zukhovitskiĭ} et al., Sov. Phys., Dokl. 13, 296--298 (1968; Zbl 0208.22002); translation from Dokl. Akad. Nauk SSSR 179, 786--789 (1968)
Zhogolev, E. A. (ed.); Klimov, G. P. (ed.); Polyak, B. T. (ed.); Berezin, I. S. (ed.) Rechenmethoden und Programmierung. 9. Sammlung von Arbeiten des Rechenzentrums der Universität Moskau. Unter Redaktion von E. A. Zhogolev, G. P. Klimov und B. T. Polyak, Gesamtleitung I. S. Berezin. (Вычислительные методы и программирование. IX. Сборник работ вычислительного Центра Московского Университета.) (Russian) Zbl 0189.17201 Moskau: Verlag der Universität. 204 S. (1967). MSC: 68-06 65-06 00B15 PDFBibTeX XML
Dynkin, E. B.; Kolgomorov, A. N.; Polyak, B. T.; Freĭdlin, M. I. Igor’ Vladimirovich Girsanov. (Russian. English translation) Zbl 0155.33304 Teor. Veroyatn. Primen. 12, 532-535 (1967); English translation in Theor. Probab. Appl. 12, 482-486 (1967). MSC: 01A70 PDFBibTeX XMLCite \textit{E. B. Dynkin} et al., Teor. Veroyatn. Primen. 12, 532--535 (1967; Zbl 0155.33304)
Zukhovitskij, S. I.; Poljak, R. A.; Primak, M. E. A numerical method for solving a convex linear programming problem in Hilbert space. (English. Russian original) Zbl 0196.51301 Sov. Math., Dokl. 6, 903-905 (1965); translation from Dokl. Akad. Nauk SSSR 163, 282-284 (1965). PDFBibTeX XMLCite \textit{S. I. Zukhovitskij} et al., Sov. Math., Dokl. 6, 903--905 (1965; Zbl 0196.51301); translation from Dokl. Akad. Nauk SSSR 163, 282--284 (1965)
Zukhovitskij, S. I.; Polyak, R. A. An algorithm for solving the problem of rational Chebyshev approximation. (English. Russian original) Zbl 0143.39003 Sov. Math., Dokl. 5, 1574-1578 (1964); translation from Dokl. Akad. Nauk SSSR 159, 726-729 (1964). PDFBibTeX XMLCite \textit{S. I. Zukhovitskij} and \textit{R. A. Polyak}, Sov. Math., Dokl. 5, 1574--1578 (1964; Zbl 0143.39003); translation from Dokl. Akad. Nauk SSSR 159, 726--729 (1964)
Zukhovitskij, S. I.; Polyak, R. A.; Primak, M. E. An algorithm for the solution of the problem of convex Cebysev approximation. (English. Russian original) Zbl 0143.17801 Sov. Math., Dokl. 4, 901-904 (1963); translation from Dokl. Akad. Nauk SSSR 151, 27-30 (1963). PDFBibTeX XMLCite \textit{S. I. Zukhovitskij} et al., Sov. Math., Dokl. 4, 901--904 (1963; Zbl 0143.17801); translation from Dokl. Akad. Nauk SSSR 151, 27--30 (1963)
Zukhovitskij, S. I.; Polyak, R. A.; Primak, M. E. An algorithm for the solution of the convex programming problem. (English. Russian original) Zbl 0137.14004 Sov. Math., Dokl. 4, 1754-1757 (1963); translation from Dokl. Akad. Nauk SSSR 153, 991-994 (1963). PDFBibTeX XMLCite \textit{S. I. Zukhovitskij} et al., Sov. Math., Dokl. 4, 1754--1757 (1963; Zbl 0137.14004); translation from Dokl. Akad. Nauk SSSR 153, 991--994 (1963)