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Polyak, Boris Teodorovich

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Author ID: polyak.boris-t Recent zbMATH articles by "Polyak, Boris Teodorovich"
Published as: Polyak, B. T.; Poljak, B. T.; Polyak, Boris T.; Polyak, Boris; Polyak, B.
External Links: MGP · Wikidata
Documents Indexed: 198 Publications since 1962, including 1 Book
2 Contributions as Editor
Biographic References: 5 Publications
Co-Authors: 70 Co-Authors with 143 Joint Publications
1,081 Co-Co-Authors
all top 5

Co-Authors

57 single-authored
32 Tsypkin, Yakov Zalmanovich
18 Shcherbakov, Pavel S.
11 Tsybakov, Alexandre B.
9 Nemirovski, Arkadi S.
7 Gryazina, Elena N.
7 Khlebnikov, Mikhail Vladimirovich
7 Kiselev, O. N.
7 Tremba, Andrey Aleksandrovich
6 Nazin, Sergey A.
5 Nazin, Aleksandr V.
4 Smirnov, Georgi V.
3 Dabbene, Fabrizio
3 Halpern, Mark E.
3 Shmulyian, S. B.
3 Topunov, Michael V.
2 Durieu, Cécile
2 Gurin, L. G.
2 Juditsky, Anatoli B.
2 Levitin, Evgeny S.
2 Panchenko, O. B.
2 Shreider, Yu. A.
2 Tempo, Roberto
2 Tret’yakov, N. V.
2 Verulava, Yu. Sh.
2 Vishnyakov, A. N.
2 Walter, Eric
1 Bakushinskĭ, Anatoliĭ Borisovich B.
1 Balashov, Maxim Viktorovich
1 Barabanov, Nikita E.
1 Belov, E. N.
1 Berezin, Ivan Semenovich
1 Borisova, T. N.
1 Calafiore, Giuseppe Carlo
1 Chernous’ko, Feliks Leonidovich
1 Chumachenko, V. V.
1 Danilova, Marina
1 Dynkin, Evgeniĭ Borisovich
1 Efremov, S. V.
1 Fatkhullin, I. F.
1 Fatkhullin, Ilyas
1 Freidlin, Mark I.
1 Gay, Paolo
1 Goldenshluger, A. V.
1 Gorgadze, Z. N.
1 Griñó, Robert
1 Jury, Eliahu I.
1 Karmanov, Vladimir G.
1 Katbab, Abdollah
1 Kılınç Karzan, Fatma
1 Klimov, G. P.
1 Kogan, Jacob
1 Kolgomorov, A. N.
1 Kulakova, Anastasiia
1 Kuntsevych, Vsevolod Mykhaĭlovych
1 Kuznetsov, O. N.
1 Kvinto, Yana I.
1 Le Hung Lan
1 Nesterov, Yurii
1 Orlov, V. S.
1 Ortega, Romeo S.
1 Petrov, N. P.
1 Pukhova, G. V.
1 Raik, Ernst V.
1 Rajk, Eh. V.
1 Rebriĭ, V. A.
1 Shalby, L. A.
1 Skokov, Viktor A.
1 Skolov, V. A.
1 Vlashek, Z.
1 Zhogolev, Evgenii Andreevich
all top 5

Serials

54 Automation and Remote Control
10 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
9 U.S.S.R. Computational Mathematics and Mathematical Physics
6 Automatica
6 IEEE Transactions on Automatic Control
6 Soviet Mathematics. Doklady
5 Soviet Physics. Doklady
4 Journal of Difference Equations and Applications
4 Doklady Mathematics
3 Problems of Information Transmission
3 Journal of Optimization Theory and Applications
3 Engineering Cybernetics
3 Systems & Control Letters
3 European Journal of Control
2 Theory of Probability and its Applications
2 Matematicheskiĭ Sbornik. Novaya Seriya
2 SIAM Journal on Control and Optimization
2 Computational Mathematics and Mathematical Physics
2 European Journal of Operational Research
2 Mathematics of the USSR, Sbornik
2 Mathematical Programming. Series A. Series B
2 International Journal of Robust and Nonlinear Control
2 Mathematical and Computer Modelling of Dynamical Systems
2 Matematicheskie Metody Resheniya Èkonomicheskikh Zadach
2 Vychislitel’nye Metody i Programmirovanie
1 Computers and Electrical Engineering
1 IEEE Transactions on Information Theory
1 International Journal of Control
1 International Journal of Systems Science
1 Teoriya Veroyatnosteĭ i eë Primeneniya
1 Avtomatika i Vychislitel ’naya Tekhnika
1 The Annals of Statistics
1 Izvestiya Akademii Nauk SSSR. Tekhnicheskaya Kibernetika
1 Journal of Soviet Mathematics
1 Kibernetika
1 Mathematics and Computers in Simulation
1 Mathematical Programming
1 Numerical Functional Analysis and Optimization
1 Soviet Journal of Automation and Information Sciences
1 Annals of Operations Research
1 International Journal of Adaptive Control and Signal Processing
1 Journal of Global Optimization
1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications
1 Problemy Peredachi Informatsii
1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika
1 SIAM Journal on Optimization
1 Set-Valued Analysis
1 Physics-Doklady
1 Mathematical Methods of Statistics
1 Journal of Mathematical Sciences (New York)
1 Nova Journal of Mathematics, Game Theory, and Algebra
1 Optimization Methods & Software
1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Applied and Computational Mathematics
1 IEEE Transactions on Circuits and Systems I: Regular Papers

Publications by Year

Citations contained in zbMATH Open

144 Publications have been cited 2,800 times in 2,314 Documents Cited by Year
The conjugate gradient method in extremal problems. Zbl 0229.49023
Polyak, B. T.
285
1971
Acceleration of stochastic approximation by averaging. Zbl 0762.62022
Polyak, B. T.; Juditsky, A. B.
200
1992
Introduction to optimization. (Vvedenie v optimizatsiyu). Zbl 0652.49002
Polyak, B. T.
167
1983
Cubic regularization of Newton method and its global performance. Zbl 1142.90500
Nesterov, Yurii; Polyak, B. T.
165
2006
Some methods of speeding up the convergence of iteration methods. Zbl 0147.35301
Poljak, B. T.
130
1967
Minimization of unsmooth functionals. Zbl 0229.65056
Polyak, B. T.
130
1971
Convergence of minimizing sequences in conditional extremum problems. Zbl 0161.07002
Levitin, E. S.; Polyak, B. T.
123
1966
A general method of solving extremum problems. Zbl 0177.15102
Polyak, B. T.
114
1967
The method of projections for finding the common point of convex sets. Zbl 0199.51002
Gurin, L. G.; Polyak, B. T.; Rajk, Eh. V.
94
1970
Constrained minimization methods. Zbl 0184.38902
Levitin, E. S.; Polyak, B. T.
93
1966
Convexity of quadratic transformations and its use in control and optimization. Zbl 0961.90074
Polyak, B. T.
82
1998
Superstable linear control systems. II: Design. Zbl 1107.93320
Polyak, B. T.; Shcherbakov, P. S.
71
2002
Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Zbl 0171.09501
Poljak, B. T.
67
1966
Ellipsoidal parameter or state estimation under model uncertainty. Zbl 1056.93063
Polyak, Boris T.; Nazin, Sergey A.; Durieu, Cécile; Walter, Eric
51
2004
New method of stochastic approximation type. Zbl 0737.93080
Polyak, B. T.
49
1990
Multi-input multi-output ellipsoidal state bounding. Zbl 1080.93656
Durieu, C.; Walter, É.; Polyak, B.
46
2001
Rejection of bounded exogenous disturbances by the method of invariant ellipsoids. Zbl 1125.93370
Nazin, S. A.; Polyak, B. T.; Topunov, M. V.
45
2007
Probabilistic robust design with linear quadratic regulators. Zbl 0974.93070
Polyak, B. T.; Tempo, R.
40
2001
Suppression of bounded exogenous disturbances: output feedback. Zbl 1156.93338
Polyak, B. T.; Topunov, M. V.
35
2008
Gradient methods for the minimisation of functionals. Zbl 0196.47701
Polyak, B. T.
35
1963
Stochastic algorithms for exact and approximate feasibility of robust LMIs. Zbl 1007.93080
Calafiore, Giuseppe; Polyak, Boris T.
32
2001
Stability regions in the parameter space: \(D\)-decomposition revisited. Zbl 1121.93028
Gryazina, Elena N.; Polyak, Boris T.
29
2006
Robust identification. Zbl 0431.93054
Poljak, B. T.; Tsypkin, Ya. Z.
26
1980
Superstable linear control systems. I: Analysis. Zbl 1094.93510
Polyak, B. T.; Shcherbakov, P. S.
21
2002
\(D\)-decomposition technique state-of-the-art. Zbl 1160.93003
Gryazina, E. N.; Polyak, B. T.; Tremba, A. A.
20
2008
Newton’s method and its use in optimization. Zbl 1123.90070
Polyak, B. T.
20
2007
Frequency domain criteria for \(l^ p\)-robust stability of continuous linear systems. Zbl 0741.93062
Tsypkin, Ya. Z.; Polyak, B. T.
19
1991
Hard problems in linear control theory: possible approaches to their solution. Zbl 1095.93011
Polyak, B. T.; Shcherbakov, P. S.
19
2005
Optimization of linear systems subject to bounded exogenous disturbances: the invariant ellipsoid technique. Zbl 1268.93062
Khlebnikov, M. V.; Polyak, B. T.; Kuntsevich, V. M.
19
2011
Convexity of nonlinear image of a small ball with applications to optimization. Zbl 1006.52001
Polyak, B. T.
18
2001
Gradient methods for solving equations and inequalities. Zbl 0147.35302
Poljak, B. T.
18
1967
Sparse feedback in linear control systems. Zbl 1327.93196
Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, P. S.
16
2014
Pseudogradient adaptation and training algorithms. Zbl 0274.93031
Polyak, B. T.; Tsypkin, Ya. Z.
16
1973
Stabilizing chaos with predictive control. Zbl 1126.93420
Polyak, B. T.
16
2005
Convexity of the reachable set of nonlinear systems under \(L_2\) bounded controls. Zbl 1050.93007
Polyak, B. T.
16
2004
Frequency criteria of robust stability and aperiodicity of linear systems. Zbl 0735.93058
Polyak, B. T.; Tsypkin, Ya. Z.
15
1990
Random algorithms for solving convex inequalities. Zbl 0997.90053
Polyak, B. T.
15
2001
Rate of convergence of nonparametric estimates of maximum-likelihood type. Zbl 0616.62048
Nemirovskij, A. S.; Polyak, B. T.; Tsybakov, A. B.
13
1985
Nonlinear programming methods in the presence of noise. Zbl 0379.90080
Poljak, B. T.
13
1978
Stability and robust stability of uniform systems. Zbl 0932.93062
Polyak, B. T.; Tsypkin, Ya. Z.
13
1996
The conjugate gradient method in extremal problems. Zbl 0191.49003
Polyak, B. T.
13
1969
Gradient projection and conditional gradient methods for constrained nonconvex minimization. Zbl 1437.49024
Balashov, M. V.; Polyak, B. T.; Tremba, A. A.
12
2020
Large deviations in linear control systems with nonzero initial conditions. Zbl 1321.93039
Polyak, B. T.; Tremba, A. A.; Khlebnikov, M. V.; Shcherbakov, P. S.; Smirnov, G. V.
12
2015
Adaptive estimation algorithms (convergence, optimality, stability). Zbl 0418.93077
Polyak, B. T.; Tsypkin, Ya. Z.
12
1979
The convexity principle and its applications. Zbl 1059.49025
Polyak, B. T.
11
2003
Filtering under nonrandom disturbances: the method of invariant ellipsoids. Zbl 1151.93032
Polyak, B. T.; Topunov, M. V.
9
2008
Optimal order of accuracy of search algorithms in stochastic optimization. Zbl 0712.90073
Polyak, B. T.; Tsybakov, A. B.
9
1990
Newton-Kantorovich method and its global convergence. Zbl 1080.65534
Polyak, B. T.
9
2006
Iterative methods for solving linear ill-posed problems under precise information. II. Zbl 0825.65041
Nemirovskij, A. S.; Polyak, B. T.
8
1984
A randomized cutting plane method with probabilistic geometric convergence. Zbl 1211.90169
Dabbene, F.; Shcherbakov, P. S.; Polyak, B. T.
8
2010
Asymptotic optimality of the \(C_ p\)-test for the orthogonal series estimation of regression. Zbl 0721.62042
Polyak, B. T.; Tsybakov, A. B.
8
1990
Iterational methods for solutions of extremal problems with equality constraints, using multipliers of Lagrange. Zbl 0217.27501
Polyak, B. T.
8
1970
Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem. Zbl 1233.65032
Nazin, A. V.; Polyak, B. T.
7
2011
Generalized superstability in control theory. Zbl 1095.93025
Polyak, B. T.
7
2004
Necessary conditions for the stability of polynomials and their use. Zbl 0854.93110
Nemirovskij, A. S.; Polyak, B. T.
7
1994
Local programming. Zbl 1040.90048
Polyak, B. T.
7
2001
Interval solutions for interval algebraic equations. Zbl 1056.65042
Polyak, B. T.; Nazin, S. A.
7
2004
On the complete instability of interval polynomials. Zbl 1118.93042
Dabbene, F.; Polyak, B. T.; Tempo, R.
7
2007
Iterative methods for solving linear ill-posed problems under precise information. I. Zbl 0825.65040
Nemirovskij, A. S.; Polyak, B. T.
6
1984
Principle component analysis: robust versions. Zbl 1392.62176
Polyak, B. T.; Khlebnikov, M. V.
6
2017
Synthesis of low-order controllers by the \(H^\infty\) and the maximum robustness criteria. Zbl 1273.93064
Kiselev, O. N.; Polyak, B. T.
6
1999
Large deviations for non-zero initial conditions in linear systems. Zbl 1348.93135
Polyak, Boris T.; Smirnov, Georgi
6
2016
Frequency domain criterion for robust stability of polytope of polynomials. Zbl 0837.93055
Tsypkin, Ya. Z.; Polyak, B. T.
6
1992
On the solution of variational inequalities. Zbl 0311.49015
Bakusinskii, A. B.; Poljak, B. T.
6
1974
Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization. Zbl 0934.93024
Polyak, Boris T.; Shcherbakov, Pavel S.
6
1999
Random spherical uncertainty in estimation and robustness. Zbl 0989.93087
Polyak, B. T.; Shcherbakov, P. S.
6
2000
Frequency criteria of robust modality in linear discrete systems. Zbl 0746.93027
Tsypkin, Ya. Z.; Polyak, B. T.
5
1990
A family of asymptotically optimal methods for choosing the order of a projective regression estimate. Zbl 0806.62031
Polyak, B. T.; Tsybakov, A. B.
5
1992
Passive stochastic approximation. Zbl 0719.62092
Nazin, A. V.; Polyak, B. T.; Tsybakov, A. B.
5
1989
Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure. Zbl 0837.93058
Polyak, B. T.; Kogan, J.
5
1995
Multidimensional stability domain of special polynomial families. Zbl 1146.93373
Gryazina, E. N.; Polyak, B. T.
5
2007
Optimal pseudogradient adaptation algorithms. Zbl 0462.49036
Polyak, B. T.; Tsypkin, Ya. Z.
5
1980
Robust pseudogradient adaptation algorithms. Zbl 0465.93094
Polyak, B. T.; Tsypkin, Ya. Z.
5
1980
Optimal design for discrete-time linear systems via new performance index. Zbl 0996.93060
Polyak, B. T.; Halpern, M. E.
5
2001
On the rate convergence of penalty functions method. Zbl 0216.54703
Polyak, B. T.
5
1971
The \(D\)-decomposition technique for linear matrix inequalities. Zbl 1195.93044
Polyak, B. T.; Shcherbakov, P. S.
4
2006
Signal processing by the non-parametric maximum-likelihood method. Zbl 0565.62028
Nemirovskij, A. S.; Polyak, B. T.; Tsybakov, A. B.
4
1984
Robust stability under complex perturbations of parameters. Zbl 0744.93078
Polyak, B. T.; Tsypkin, Ya. Z.
4
1991
Ellipsoidal estimation with respect to a generalized criterion. Zbl 0749.93021
Kiselev, O. N.; Polyak, B. T.
4
1991
Peak effects in stable linear difference equations. Zbl 1403.39002
Polyak, B. T.; Shcherbakov, P. S.; Smirnov, G.
4
2018
Regularization-based solution of the PageRank problem for large matrices. Zbl 1268.93014
Polyak, B. T.; Tremba, A. A.
4
2012
Subgradient methods: A survey of Soviet research. Zbl 0407.90072
Poljak, B. T.
4
1978
Convergence and convergence rate of iterative stochastic algorithms. II: The linear case. Zbl 0415.93062
Polyak, B. T.
4
1977
Interval parameter estimation under model uncertainty. Zbl 1122.93024
Nazin, Sergey A.; Polyak, Boris T.
4
2005
Robust Nyquist test. Zbl 0796.93095
Polyak, B. T.; Tsypkin, Ya. Z.
4
1992
Recursive algorithms for inner ellipsoidal approximation of convex polytopes. Zbl 1034.93018
Dabbene, Fabrizio; Gay, Paolo; Polyak, Boris T.
4
2003
Robust linear algebra and robust aperiodicity. Zbl 1049.93021
Polyak, Boris T.
4
2003
Convergence of methods of feasible directions in extremal problems. Zbl 0255.90053
Poljak, B. T.
3
1973
Accuracy guaranties for \(\ell_{1}\) recovery of block-sparse signals. Zbl 1296.62088
Juditsky, Anatoli; Karzan, Fatma Kılınç; Nemirovski, Arkadi; Polyak, Boris
3
2012
Design of the low-order controllers by the \(H_{\infty }\) criterion: a parametric approach. Zbl 1125.93343
Gryazina, E. N.; Polyak, B. T.; Tremba, A. A.
3
2007
History of mathematical programming in the USSR: Analyzing the phenomenon. Zbl 1030.90001
Polyak, B. T.
3
2002
Robust stability of discrete linear systems. Zbl 0752.93056
Polyak, B. T.; Tsypkin, Ya. Z.
3
1991
Robustness analysis for multilinear perturbations. Zbl 0771.93020
Polyak, B. T.
3
1992
On stochastic approximation with arbitrary noise (the KW-case). Zbl 0774.62087
Polyak, B. T.; Tsybakov, A. B.
3
1992
Convergence and convergence rate of iterative stochastic algorithms. I: General case. Zbl 0363.93054
Poljak, B. T.
3
1976
Robust identification. Zbl 0392.93037
Polyak, B. T.; Tsypkin, Ya. Z.
3
1978
Frequency responses under parametric uncertainty. Zbl 0922.93027
Kiselev, O. N.; Lan, Le Hung; Polyak, B. T.
3
1997
High-gain robust control. Zbl 0933.93033
Tsypkin, Ya. Z.; Polyak, B. T.
3
1999
Construction of value set for robustness analysis via circular arithmetic. Zbl 0796.93096
Polyak, B. T.; Scherbakov, P. S.; Shmulyian, S. B.
3
1994
Halbstetigkeit von Integral-Funktionalen und Existenzsätze für Extremalprobleme. Zbl 0164.42302
Poljak, B. T.
3
1969
Linear matrix inequalities in control systems with uncertainty. Zbl 1460.93056
Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, P. S.
2
2021
Optimizing static linear feedback: gradient method. Zbl 1475.49039
Fatkhullin, Ilyas; Polyak, Boris
2
2021
Static controller synthesis for peak-to-peak gain minimization as an optimization problem. Zbl 1475.93042
Polyak, B. T.; Khlebnikov, M. V.
1
2021
Gradient projection and conditional gradient methods for constrained nonconvex minimization. Zbl 1437.49024
Balashov, M. V.; Polyak, B. T.; Tremba, A. A.
12
2020
New versions of Newton method: step-size choice, convergence domain and under-determined equations. Zbl 1464.90112
Polyak, Boris; Tremba, Andrey
2
2020
Sparse solutions of optimal control via Newton method for under-determined systems. Zbl 1437.49043
Polyak, Boris; Tremba, Andrey
2
2020
Non-monotone behavior of the heavy ball method. Zbl 1445.39002
Danilova, Marina; Kulakova, Anastasiia; Polyak, Boris
1
2020
Peak effects in stable linear difference equations. Zbl 1403.39002
Polyak, B. T.; Shcherbakov, P. S.; Smirnov, G.
4
2018
Optimisation and asymptotic stability. Zbl 1403.93169
Polyak, Boris T.; Shcherbakov, P. S.
1
2018
Principle component analysis: robust versions. Zbl 1392.62176
Polyak, B. T.; Khlebnikov, M. V.
6
2017
Stability and synchronization of oscillators: new Lyapunov functions. Zbl 1373.93250
Polyak, Boris T.; Kvinto, Yana I.
2
2017
Convexity/nonconvexity certificates for power flow analysis. Zbl 1397.90080
Polyak, Boris; Gryazina, Elena
1
2017
Large deviations for non-zero initial conditions in linear systems. Zbl 1348.93135
Polyak, Boris T.; Smirnov, Georgi
6
2016
Stability study of a power system with unipolar electromagnetic brake. Zbl 1354.93134
Polyak, B. T.; Kuznetsov, O. N.; Chumachenko, V. V.
1
2016
On existence and stability of equilibria of linear time-invariant systems with constant power loads. Zbl 1468.93145
Barabanov, Nikita; Ortega, Romeo; Griñó, Robert; Polyak, Boris
1
2016
Large deviations in linear control systems with nonzero initial conditions. Zbl 1321.93039
Polyak, B. T.; Tremba, A. A.; Khlebnikov, M. V.; Shcherbakov, P. S.; Smirnov, G. V.
12
2015
Sparse feedback in linear control systems. Zbl 1327.93196
Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, P. S.
16
2014
Random sampling: billiard walk algorithm. Zbl 1338.60190
Gryazina, Elena; Polyak, Boris
1
2014
Regularization-based solution of the PageRank problem for large matrices. Zbl 1268.93014
Polyak, B. T.; Tremba, A. A.
4
2012
Accuracy guaranties for \(\ell_{1}\) recovery of block-sparse signals. Zbl 1296.62088
Juditsky, Anatoli; Karzan, Fatma Kılınç; Nemirovski, Arkadi; Polyak, Boris
3
2012
Optimization of linear systems subject to bounded exogenous disturbances: the invariant ellipsoid technique. Zbl 1268.93062
Khlebnikov, M. V.; Polyak, B. T.; Kuntsevich, V. M.
19
2011
Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem. Zbl 1233.65032
Nazin, A. V.; Polyak, B. T.
7
2011
Randomized methods based on new Monte Carlo schemes for control and optimization. Zbl 1233.90281
Polyak, Boris T.; Gryazina, Elena N.
2
2011
A randomized cutting plane method with probabilistic geometric convergence. Zbl 1211.90169
Dabbene, F.; Shcherbakov, P. S.; Polyak, B. T.
8
2010
The randomized algorithm for finding an eigenvector of the stochastic matrix with application to PageRank. Zbl 1176.65042
Nazin, A. V.; Polyak, B. T.
1
2009
Suppression of bounded exogenous disturbances: output feedback. Zbl 1156.93338
Polyak, B. T.; Topunov, M. V.
35
2008
\(D\)-decomposition technique state-of-the-art. Zbl 1160.93003
Gryazina, E. N.; Polyak, B. T.; Tremba, A. A.
20
2008
Filtering under nonrandom disturbances: the method of invariant ellipsoids. Zbl 1151.93032
Polyak, B. T.; Topunov, M. V.
9
2008
Rejection of bounded exogenous disturbances by the method of invariant ellipsoids. Zbl 1125.93370
Nazin, S. A.; Polyak, B. T.; Topunov, M. V.
45
2007
Newton’s method and its use in optimization. Zbl 1123.90070
Polyak, B. T.
20
2007
On the complete instability of interval polynomials. Zbl 1118.93042
Dabbene, F.; Polyak, B. T.; Tempo, R.
7
2007
Multidimensional stability domain of special polynomial families. Zbl 1146.93373
Gryazina, E. N.; Polyak, B. T.
5
2007
Design of the low-order controllers by the \(H_{\infty }\) criterion: a parametric approach. Zbl 1125.93343
Gryazina, E. N.; Polyak, B. T.; Tremba, A. A.
3
2007
Ellipsoid-based parametric estimation in the linear multidimensional systems with uncertain model description. Zbl 1142.93308
Nazin, S. A.; Polyak, B. T.
1
2007
Cubic regularization of Newton method and its global performance. Zbl 1142.90500
Nesterov, Yurii; Polyak, B. T.
165
2006
Stability regions in the parameter space: \(D\)-decomposition revisited. Zbl 1121.93028
Gryazina, Elena N.; Polyak, Boris T.
29
2006
Newton-Kantorovich method and its global convergence. Zbl 1080.65534
Polyak, B. T.
9
2006
The \(D\)-decomposition technique for linear matrix inequalities. Zbl 1195.93044
Polyak, B. T.; Shcherbakov, P. S.
4
2006
Hard problems in linear control theory: possible approaches to their solution. Zbl 1095.93011
Polyak, B. T.; Shcherbakov, P. S.
19
2005
Stabilizing chaos with predictive control. Zbl 1126.93420
Polyak, B. T.
16
2005
Interval parameter estimation under model uncertainty. Zbl 1122.93024
Nazin, Sergey A.; Polyak, Boris T.
4
2005
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. Zbl 1080.93502
2
2005
Ellipsoidal parameter or state estimation under model uncertainty. Zbl 1056.93063
Polyak, Boris T.; Nazin, Sergey A.; Durieu, Cécile; Walter, Eric
51
2004
Convexity of the reachable set of nonlinear systems under \(L_2\) bounded controls. Zbl 1050.93007
Polyak, B. T.
16
2004
Generalized superstability in control theory. Zbl 1095.93025
Polyak, B. T.
7
2004
Interval solutions for interval algebraic equations. Zbl 1056.65042
Polyak, B. T.; Nazin, S. A.
7
2004
On the convergence of outer ellipsoidal approximations of attainability domains of linear discrete dynamical systems. Zbl 1078.93006
Nazin, A. V.; Nazin, S. A.; Polyak, B. T.
2
2004
The convexity principle and its applications. Zbl 1059.49025
Polyak, B. T.
11
2003
Recursive algorithms for inner ellipsoidal approximation of convex polytopes. Zbl 1034.93018
Dabbene, Fabrizio; Gay, Paolo; Polyak, Boris T.
4
2003
Robust linear algebra and robust aperiodicity. Zbl 1049.93021
Polyak, Boris T.
4
2003
Superstable linear control systems. II: Design. Zbl 1107.93320
Polyak, B. T.; Shcherbakov, P. S.
71
2002
Superstable linear control systems. I: Analysis. Zbl 1094.93510
Polyak, B. T.; Shcherbakov, P. S.
21
2002
History of mathematical programming in the USSR: Analyzing the phenomenon. Zbl 1030.90001
Polyak, B. T.
3
2002
Optimization-based design of fixed-order controllers for command following. Zbl 1009.93029
Halpern, Mark E.; Polyak, Boris T.
1
2002
Multi-input multi-output ellipsoidal state bounding. Zbl 1080.93656
Durieu, C.; Walter, É.; Polyak, B.
46
2001
Probabilistic robust design with linear quadratic regulators. Zbl 0974.93070
Polyak, B. T.; Tempo, R.
40
2001
Stochastic algorithms for exact and approximate feasibility of robust LMIs. Zbl 1007.93080
Calafiore, Giuseppe; Polyak, Boris T.
32
2001
Convexity of nonlinear image of a small ball with applications to optimization. Zbl 1006.52001
Polyak, B. T.
18
2001
Random algorithms for solving convex inequalities. Zbl 0997.90053
Polyak, B. T.
15
2001
Local programming. Zbl 1040.90048
Polyak, B. T.
7
2001
Optimal design for discrete-time linear systems via new performance index. Zbl 0996.93060
Polyak, B. T.; Halpern, M. E.
5
2001
Minimization of overshoot in linear discrete-time systems via low-order controllers. Zbl 1092.93538
Kiselev, O. N.; Polyak, B. T.
1
2001
Random spherical uncertainty in estimation and robustness. Zbl 0989.93087
Polyak, B. T.; Shcherbakov, P. S.
6
2000
Synthesis of low-order controllers by the \(H^\infty\) and the maximum robustness criteria. Zbl 1273.93064
Kiselev, O. N.; Polyak, B. T.
6
1999
Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization. Zbl 0934.93024
Polyak, Boris T.; Shcherbakov, Pavel S.
6
1999
High-gain robust control. Zbl 0933.93033
Tsypkin, Ya. Z.; Polyak, B. T.
3
1999
Robust stability and design of linear discrete-time SISO systems under \(l_1\) uncertainties. Zbl 0955.93023
Polyak, Boris T.; Halpern, Mark E.
2
1999
Convexity of quadratic transformations and its use in control and optimization. Zbl 0961.90074
Polyak, B. T.
82
1998
Frequency responses under parametric uncertainty. Zbl 0922.93027
Kiselev, O. N.; Lan, Le Hung; Polyak, B. T.
3
1997
Stability and robust stability of uniform systems. Zbl 0932.93062
Polyak, B. T.; Tsypkin, Ya. Z.
13
1996
Multiplying disks: Robust stability of a cascade connection. Zbl 0868.93051
Polyak, B. T.; Vishnyakov, A. N.
2
1996
A probabilistic approach to robust stability of time delay systems. Zbl 0931.93053
Polyak, B. T.; Shcherbakov, P. S.
1
1996
Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure. Zbl 0837.93058
Polyak, B. T.; Kogan, J.
5
1995
Frequency domain criteria for robust stability of a family of linear difference equations. Zbl 0863.39006
Tsypkin, Ya. Z.; Polyak, B. T.
1
1995
Necessary conditions for the stability of polynomials and their use. Zbl 0854.93110
Nemirovskij, A. S.; Polyak, B. T.
7
1994
Construction of value set for robustness analysis via circular arithmetic. Zbl 0796.93096
Polyak, B. T.; Scherbakov, P. S.; Shmulyian, S. B.
3
1994
On the strict- and wide-sense stability robustness of uncertain systems: Application of a new frequency criterion. Zbl 0818.93052
Tsypkin, Ya. Z.; Polyak, B. T.; Katbab, A.; Jury, E. I.
2
1994
Circular arithmetic and its applications in robustness analysis. Zbl 0828.65045
Polyak, B.; Scherbakov, P.; Shmulyian, S.
1
1994
Robust absolute stability of continuous systems. Zbl 0792.93104
Tsypkin, Ya. Z.; Polyak, B. T.
1
1993
Estimation of regression parameters with arbitrary noise. Zbl 0798.62075
Goldenshluger, A. V.; Polyak, B. T.
1
1993
Robust stability of a chain of simple links. Zbl 0825.93596
Kiselev, O. N.; Polyak, B. T.
1
1993
Acceleration of stochastic approximation by averaging. Zbl 0762.62022
Polyak, B. T.; Juditsky, A. B.
200
1992
Frequency domain criterion for robust stability of polytope of polynomials. Zbl 0837.93055
Tsypkin, Ya. Z.; Polyak, B. T.
6
1992
A family of asymptotically optimal methods for choosing the order of a projective regression estimate. Zbl 0806.62031
Polyak, B. T.; Tsybakov, A. B.
5
1992
Robust Nyquist test. Zbl 0796.93095
Polyak, B. T.; Tsypkin, Ya. Z.
4
1992
Robustness analysis for multilinear perturbations. Zbl 0771.93020
Polyak, B. T.
3
1992
On stochastic approximation with arbitrary noise (the KW-case). Zbl 0774.62087
Polyak, B. T.; Tsybakov, A. B.
3
1992
Robust absolute stability of continuous systems. Zbl 0771.93069
Tsypkin, Ya. Z.; Polyak, B. T.
2
1992
Optimal and robust kernel algorithms for passive stochastic approximation. Zbl 0753.62053
Nazin, A. V.; Polyak, B. T.; Tsybakov, A. B.
1
1992
Frequency domain criteria for \(l^ p\)-robust stability of continuous linear systems. Zbl 0741.93062
Tsypkin, Ya. Z.; Polyak, B. T.
19
1991
Robust stability under complex perturbations of parameters. Zbl 0744.93078
Polyak, B. T.; Tsypkin, Ya. Z.
4
1991
Ellipsoidal estimation with respect to a generalized criterion. Zbl 0749.93021
Kiselev, O. N.; Polyak, B. T.
4
1991
Robust stability of discrete linear systems. Zbl 0752.93056
Polyak, B. T.; Tsypkin, Ya. Z.
3
1991
Robust \(D\)-partition. Zbl 0793.93096
Petrov, N. P.; Polyak, B. T.
2
1991
New method of stochastic approximation type. Zbl 0737.93080
Polyak, B. T.
49
1990
Frequency criteria of robust stability and aperiodicity of linear systems. Zbl 0735.93058
Polyak, B. T.; Tsypkin, Ya. Z.
15
1990
Optimal order of accuracy of search algorithms in stochastic optimization. Zbl 0712.90073
Polyak, B. T.; Tsybakov, A. B.
9
1990
Asymptotic optimality of the \(C_ p\)-test for the orthogonal series estimation of regression. Zbl 0721.62042
Polyak, B. T.; Tsybakov, A. B.
8
1990
Frequency criteria of robust modality in linear discrete systems. Zbl 0746.93027
Tsypkin, Ya. Z.; Polyak, B. T.
5
1990
Passive stochastic approximation. Zbl 0719.62092
Nazin, A. V.; Polyak, B. T.; Tsybakov, A. B.
5
1989
...and 44 more Documents
all top 5

Cited by 2,996 Authors

52 Polyak, Boris Teodorovich
24 Toint, Philippe L.
23 Khlebnikov, Mikhail Vladimirovich
17 Tempo, Roberto
16 Cartis, Coralia
16 Kumam, Poom
16 Shcherbakov, Pavel S.
15 Babaie-Kafaki, Saman
15 Nesterov, Yurii
15 Sherali, Hanif D.
14 Andrei, Neculai
14 Balashov, Maxim Viktorovich
13 Gould, Nicholas Ian Mark
13 Li, Guoyin
13 Martínez, José Mario
13 Poznyak, Aleksandr Semënovich
12 Bauschke, Heinz H.
12 Censor, Yair
12 Yang, Xiaoqi
11 Dabbene, Fabrizio
11 Gasnikov, Alexander V.
11 Tremba, Andrey Aleksandrovich
11 Wei, Zengxin
10 Aida-Zade, Kamil Rajab
10 Attouch, Hedy
10 Combettes, Patrick L.
10 Dai, Yu-Hong
10 Duchi, John C.
10 Grapiglia, Geovani Nunes
10 Ryabchenko, Vladimir Nikolaevich
10 Shi, Zhenjun
9 Amiri, Ali
9 Bala Abubakar, Auwal
9 Cho, Yeol Je
9 Iusem, Alfredo Noel
9 Konnov, Igor V.
9 Yuan, Gonglin
9 Yuan, Ya-xiang
9 Zhou, Weijun
8 Beck, Amir
8 Bello Cruz, Jose Yunier
8 Birgin, Ernesto G.
8 Dai, Zhifeng
8 Gibali, Aviv
8 Holmberg, Kaj
8 Hu, Yaohua
8 Lan, Guanghui
8 Nedić, Angelia
8 Noor, Muhammad Aslam
8 Wang, Shawn Xianfu
7 Álamo, Teodoro
7 Fursov, A. S.
7 Granichin, Oleg N.
7 Gryazina, Elena N.
7 Jeyakumar, Vaithilingam
7 Jordan, Michael Irwin
7 Liu, Zexian
7 Misrikhanov, M. Sh.
7 Nikodem, Kazimierz
7 Reich, Simeon
7 Svaiter, Benar Fux
7 Tsykunov, A. M.
7 Xia, Yong
6 Anh, Lam Quoc
6 Bach, Francis R.
6 Bertsekas, Dimitri Panteli
6 Calafiore, Giuseppe Carlo
6 Crombez, Gilbert
6 Curtis, Frank E.
6 Farid, Ghulam
6 Fort, Gersende
6 Ghanbari, Reza
6 Huang, Xuexiang
6 Ibrahim, Abdulkarim Hassan
6 Jian, Jinbao
6 Jiang, Xianzhen
6 Kim, Sehun
6 Kuntsevych, Vsevolod Mykhaĭlovych
6 Larsson, Torbjörn
6 Li, Donghui
6 Liu, Jinkui
6 Malikov, A. I.
6 Mera, Manuel
6 Mikrin, Evgeniĭ Anatol’evich
6 Nazin, Aleksandr V.
6 Patriksson, Michael
6 Peng, Jianwen
6 Polyak, Roman A.
6 Popkov, Alexey Yu.
6 Raydan, Marcos
6 Rehman, Habib Ur
6 Robinson, Daniel P.
6 Sellami, Badreddine
6 Shanbhag, Uday V.
6 Walter, Eric
6 Yarullin, Rashid Samatovich
6 Zubov, N. E.
5 Abdullayev, Vaqif M.
5 Amini, Keyvan
5 Butnariu, Dan
...and 2,896 more Authors
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Cited in 338 Serials

164 Automation and Remote Control
121 Journal of Optimization Theory and Applications
110 Mathematical Programming. Series A. Series B
98 Automatica
72 SIAM Journal on Optimization
58 European Journal of Operational Research
54 Applied Mathematics and Computation
49 Computational Optimization and Applications
46 Journal of Computational and Applied Mathematics
46 Optimization Methods & Software
45 Journal of Computer and Systems Sciences International
37 Numerical Algorithms
34 Journal of Mathematical Analysis and Applications
34 Optimization
33 Journal of Global Optimization
30 Cybernetics and Systems Analysis
30 Journal of Inequalities and Applications
27 Systems & Control Letters
25 Optimization Letters
24 Mathematical Programming
24 Numerical Functional Analysis and Optimization
22 International Journal of Control
22 The Annals of Statistics
22 Computational Mathematics and Mathematical Physics
19 Mathematical Problems in Engineering
18 Computational and Applied Mathematics
18 Doklady Mathematics
17 Computers & Mathematics with Applications
17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
17 Cybernetics
17 Annals of Operations Research
15 Abstract and Applied Analysis
14 Applied Mathematics and Optimization
14 Operations Research Letters
14 Computers & Operations Research
14 Journal of Mathematical Sciences (New York)
13 Numerische Mathematik
13 International Journal of Robust and Nonlinear Control
13 Journal of Applied Mathematics
13 Journal of Machine Learning Research (JMLR)
12 Computational Mathematics and Modeling
12 Linear Algebra and its Applications
12 Fixed Point Theory and Applications
12 Proceedings of the Steklov Institute of Mathematics
11 European Journal of Control
11 Set-Valued and Variational Analysis
10 Journal of the Franklin Institute
10 Journal of Soviet Mathematics
10 Applied Numerical Mathematics
10 Mathematical Methods of Operations Research
10 Journal of Mathematics
9 Computer Methods in Applied Mechanics and Engineering
9 Kybernetika
9 International Journal of Adaptive Control and Signal Processing
9 Differential Equations
8 Journal of Differential Equations
8 Russian Mathematics
8 Positivity
8 AIMS Mathematics
7 Mathematical Notes
7 Calcolo
7 Journal of Scientific Computing
7 Stochastic Processes and their Applications
7 Journal of Industrial and Management Optimization
7 International Journal of Systems Science. Principles and Applications of Systems and Integration
6 Mathematics of Computation
6 Mathematics of Operations Research
6 SIAM Journal on Control and Optimization
6 Acta Applicandae Mathematicae
6 Journal of Complexity
6 Complexity
6 Optimization and Engineering
6 Lobachevskii Journal of Mathematics
6 Journal of Fixed Point Theory and Applications
6 Electronic Journal of Statistics
6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
5 Discrete Applied Mathematics
5 Journal of Computational Physics
5 Moscow University Mechanics Bulletin
5 Ukrainian Mathematical Journal
5 Computing
5 Information Sciences
5 Journal of Statistical Planning and Inference
5 International Journal of Computer Mathematics
5 SIAM Journal on Scientific Computing
5 Mathematical Methods of Statistics
5 Bernoulli
5 Vietnam Journal of Mathematics
5 Journal of Systems Science and Complexity
5 Journal of Applied Mathematics and Computing
5 Journal of Nonlinear Science and Applications
5 SIAM Journal on Mathematics of Data Science
4 Inverse Problems
4 Metrika
4 Mathematics and Computers in Simulation
4 Operations Research
4 Acta Mathematicae Applicatae Sinica. English Series
4 Probability Theory and Related Fields
4 Mathematical and Computer Modelling
4 Machine Learning
...and 238 more Serials
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Cited in 52 Fields

1,232 Operations research, mathematical programming (90-XX)
751 Numerical analysis (65-XX)
565 Systems theory; control (93-XX)
409 Calculus of variations and optimal control; optimization (49-XX)
209 Statistics (62-XX)
160 Operator theory (47-XX)
149 Computer science (68-XX)
65 Probability theory and stochastic processes (60-XX)
57 Real functions (26-XX)
55 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
51 Ordinary differential equations (34-XX)
49 Linear and multilinear algebra; matrix theory (15-XX)
49 Functional analysis (46-XX)
39 Partial differential equations (35-XX)
38 Information and communication theory, circuits (94-XX)
36 Convex and discrete geometry (52-XX)
28 Difference and functional equations (39-XX)
26 Dynamical systems and ergodic theory (37-XX)
24 Approximations and expansions (41-XX)
21 Global analysis, analysis on manifolds (58-XX)
17 General topology (54-XX)
17 Mechanics of deformable solids (74-XX)
14 Mechanics of particles and systems (70-XX)
14 Biology and other natural sciences (92-XX)
6 Optics, electromagnetic theory (78-XX)
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4 History and biography (01-XX)
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3 General and overarching topics; collections (00-XX)
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2 Mathematical logic and foundations (03-XX)
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1 Order, lattices, ordered algebraic structures (06-XX)
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1 Geophysics (86-XX)

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