Boris T. Polyak

Boris T. Polyak's AcademicInfluence.com Rankings

Boris T. Polyak

Mathematics

#4915

World Rank

#6942

Historical Rank

Control Theory

#17

World Rank

#18

Historical Rank

Applied Mathematics

#102

World Rank

#116

Historical Rank

Measure Theory

#509

World Rank

#718

Historical Rank

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Mathematics

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Boris T. Polyak's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Some methods of speeding up the convergence of iteration methods (1964) (2156)
Acceleration of stochastic approximation by averaging (1992) (1766)
Cubic regularization of Newton method and its global performance (2006) (869)
The conjugate gradient method in extremal problems (1969) (834)
The method of projections for finding the common point of convex sets (1967) (785)
Constrained minimization methods (1966) (780)
Minimization of unsmooth functionals (1969) (552)
B.S. Mordukhovich. Variational Analysis and Generalized Differentiation. I. Basic Theory, II. Applications (2009) (343)
The conjugate gradient method in extreme problems (2015) (251)
Ellipsoidal parameter or state estimation under model uncertainty (2004) (245)
Multi-Input Multi-Output Ellipsoidal State Bounding (2001) (244)
Convexity of Quadratic Transformations and Its Use in Control and Optimization (1998) (211)
Gradient methods for the minimisation of functionals (1963) (199)
Probabilistic robust design with linear quadratic regulators (2000) (187)
Stability regions in the parameter space: D-decomposition revisited (2006) (138)
Rejection of bounded exogenous disturbances by the method of invariant ellipsoids (2007) (133)
Stochastic algorithms for exact and approximate feasibility of robust LMIs (2001) (130)
Newton's method and its use in optimization (2007) (120)
Frequency domain criteria for l/sup p/-robust stability of continuous linear systems (1991) (104)
An LMI approach to structured sparse feedback design in linear control systems (2013) (103)
D-decomposition technique state-of-the-art (2008) (89)
Suppression of bounded exogenous disturbances: Output feedback (2008) (89)
On Existence and Stability of Equilibria of Linear Time-Invariant Systems With Constant Power Loads (2016) (86)
Gradient methods for solving equations and inequalities (1964) (79)
Optimization of linear systems subject to bounded exogenous disturbances: The invariant ellipsoid technique (2011) (74)
Random Algorithms for Solving Convex Inequalities (2001) (69)
Hard Problems in Linear Control Theory: Possible Approaches to Solution (2005) (65)
Mixed LMI/randomized methods for static output feedback control design (2010) (64)
STABILITY AND ROBUST STABILITY OF UNIFORM SYSTEMS (1996) (60)
Superstable Linear Control Systems. I. Analysis (2002) (54)
RACT: Randomized Algorithms Control Toolbox for MATLAB (2008) (49)
Stabilizing Chaos with Predictive Control (2005) (49)
Convexity of Nonlinear Image of a Small Ball with Applications to Optimization (2001) (48)
A Randomized Cutting Plane Method with Probabilistic Geometric Convergence (2010) (47)
Newton-Kantorovich Method and Its Global Convergence (2006) (46)
Trace Versus Determinant in Ellipsoidal Outer-Bounding, with Application to State Estimation (1996) (44)
Lyapunov Functions: An Optimization Theory Perspective (2017) (40)
Iterative methods using lagrange multipliers for solving extremal problems with constraints of the equation type (1970) (40)
Optimizing Static Linear Feedback: Gradient Method (2020) (38)
Superstable Linear Control Systems. II. Design (2002) (37)
Rejection of Bounded Disturbances via Invariant Ellipsoids Technique (2006) (37)
Asymptotic Optimality of the $C_p$-Test for the Orthogonal Series Estimation of Regression (1991) (36)
The convergence rate of the penalty function method (1971) (33)
Large deviations in linear control systems with nonzero initial conditions (2015) (31)
Random spherical uncertainty in estimation and robustness (2000) (30)
Sparse feedback in linear control systems (2014) (29)
Interval parameter estimation under model uncertainty (2005) (29)
Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure (1995) (28)
CONVEXITY OF THE REACHABLE SET OF NONLINEAR SYSTEMS UNDER L 2 BOUNDED CONTROLS (27)
Accuracy guaranties for ` 1 recovery of block-sparse signals (2012) (26)
Large deviations for non-zero initial conditions in linear systems (2016) (26)
Gradient Projection and Conditional Gradient Methods for Constrained Nonconvex Minimization (2019) (25)
The convexity principle and its applications (2003) (25)
Optimal design for discrete‐time linear systems via new performance index (2001) (25)
Interval solutions for interval algebraic equations (2004) (23)
Fast algorithms for exact and approximate feasibility of robust LMIs (2000) (23)
A New Approach to Open Robustness Problems Based on Probabilistic Prediction Formulae (1996) (23)
Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem (2011) (22)
On the Complete Instability of Interval Polynomials (2006) (22)
Random sampling: Billiard Walk algorithm (2012) (22)
Frequency Domain Criterion for Robust Stability of Polytope of Polynomials (2020) (21)
DESIGN OF LOW-ORDER CONTROLLERS BY THE H AND MAXIMAL-ROBUSTNESS PERFORMANCE INDICES (1999) (20)
History of mathematical programming in the USSR: analyzing the phenomenon (2002) (20)
Principle component analysis: Robust versions (2017) (20)
Robust eigenvector of a stochastic matrix with application to PageRank (2012) (19)
Robustness Analysis for Multilinear Perturbations (1992) (19)
Billiard walk - a new sampling algorithm for control and optimization (2014) (18)
Regularization-based solution of the PageRank problem for large matrices (2012) (18)
The D-decomposition technique for linear matrix inequalities (2006) (18)
On Existence of Equilibria of Multi-Port Linear AC Networks With Constant-Power Loads (2017) (17)
Recursive algorithms for inner ellipsoidal approximation of convex polytopes (2003) (17)
The use of a new optimization criterion for discrete-time feedback controller design (1999) (17)
Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization (1998) (17)
Hit-and-Run: new design technique for stabilization, robustness and optimization of linear systems (2008) (16)
Extended Superstability in Control Theory (2004) (16)
New versions of Newton method: step-size choice, convergence domain and under-determined equations (2017) (16)
Adaptive randomized algorithm for finding eigenvector of stochastic matrix with application to PageRank (2009) (16)
On stochastic approximation with arbitrary noise (the KW-case) (1992) (15)
Ellipsoidal approximations to attraction domains of linear systems with bounded control (2009) (15)
Robust Absolute Stability of Continuous Systems (1993) (15)
Invariant Ellipsoids Approach to Robust Rejection of Persistent Disturbances (2008) (14)
Non-monotone Behavior of the Heavy Ball Method (2018) (13)
PageRank: new regularizations and simulation models (2011) (13)
Robust Linear Algebra and Robust Aperiodicity (2003) (13)
Frequency domain criteria for robust stability of bivariate polynomials (1994) (13)
Fixed-order controller design for SISO systems using Monte Carlo technique (2007) (13)
FREQUENCY RESPONSES UNDER PARAMETRIC UNCERTAINTY (1997) (13)
Special issue on the set membership modelling of uncertainties in dynamical systems (2005) (12)
Convexity/Nonconvexity Certificates for Power Flow Analysis (2017) (12)
ELLIPSOIDAL ESTIMATION UNDER MODEL UNCERTAINTY (2002) (11)
Accuracy guaranties for $\ell_1$ recovery of block-sparse signals (2011) (11)
Set-Membership Estimation with the Trace Criterion made Simpler than with the Determinant Criterion (2000) (11)
Construction of value set for robustness analysis via circular arithmetic (1994) (11)
ON THE ROOT INVARIANT REGIONS STRUCTURE FOR LINEAR SYSTEMS (2005) (11)
Design of the low-order controllers by the H∞ criterion: A parametric approach (2007) (10)
Sparse solutions of optimal control via Newton method for under-determined systems (2019) (10)
Randomized methods based on new Monte Carlo schemes for control and optimization (2011) (10)
Cubic regularization of a Newton scheme and its global performance (2003) (10)
Peak effects in stable linear difference equations (2018) (10)
Optimisation and asymptotic stability (2018) (9)
Markov Chain Monte Carlo method exploiting barrier functions with applications to control and optimization (2010) (9)
Filtering under nonrandom disturbances: the method of invariant ellipsoids (2008) (9)
The volumetric singular value and robustness of feedback control systems (1993) (9)
High-Gain Robust Control (1999) (9)
Controlling chaos by predictive control (2005) (9)
Robust Principal Component Analysis: An IRLS Approach (2017) (8)
Linear Matrix Inequalities in Control Systems with Uncertainty (2021) (8)
Robust stability and design of linear discrete-time SISO systems under l1 uncertainties (1999) (8)
Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems - Survey (2022) (8)
Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems? (2016) (8)
Convergence of methods of feasible directions in extremal problems (1971) (8)
A randomized cutting plane scheme with geometric convergence: Probabilistic analysis and SDP applications (2008) (7)
A randomized algorithm for finding eigenvector of stochastic matrix with application to PageRank problem (2009) (7)
Multiplying Disks: Robust Stability of a Cascade Connection (1996) (7)
Transient Response in Matrix Discrete-Time Linear Systems (2019) (7)
Multidimensional stability domain of special polynomial families (2007) (7)
Solving underdetermined nonlinear equations by Newton-like method (2017) (6)
Estimation of Parameters in Linear Multidimensional Systems under Interval Uncertainty (2006) (6)
On the accuracy of l1-filtering of signals with block-sparse structure (2011) (6)
Invariant Sets of Nonlinear Discrete Systems with Bounded Disturbances and Control Problems (2009) (6)
Optimal and robust kernel algorithms for passive stochastic approximation (1992) (6)
Frequency domain criteria for robust stability of a family of linear difference equations 1 (1995) (6)
Stability and synchronization of oscillators: New Lyapunov functions (2017) (6)
A randomized method for solving semidefinite programs (2007) (5)
Limiting Behaviour of Bounding Ellipsoids for State Estimation (2001) (5)
Optimization-based design of fixed-order controllers for command following (2002) (5)
Special weighting and objective functions for robust synthesis with a type of coprime factor uncertainty model (1994) (5)
Optimal recurrent algorithms for identification of nonstationary plants (1987) (5)
Minimization methods with constraints (1976) (5)
Textbook of a New Type Review of the Book of B.R. Andrievskii and A.L. Fradkov “Elements of Mathematical Modeling in the MATLAB 5 and Scilab Software Environments” (St. Petersburg: Nauka, 2001) (2001) (4)
A superstability approach to synthesizing low order suboptimal L/sub /spl infin//-induced controllers for LPV systems (2002) (4)
ROBUST STABILITY OF DISCRETE LINEAR SYSTEMS (1991) (4)
On Convergence of External Ellipsoidal Approximations of the Reachability Domains of Discrete Dynamic Linear Systems (2004) (4)
Large deviations in continuous-time linear single-input control systems (2014) (4)
Inner ellipsoidal approximation of membership set: a fast recursive algorithm (2000) (4)
A Family of Asymptotically Optimal Methods for Choosing the Order of a Projective Regression Estimate (1993) (4)
Optimal tracking with fixed order controllers (2000) (4)
On the strict and wide-sense stability robustness of uncertain systems-application of a new frequency criterion (1991) (4)
Adaptive and Robust Control in the USSR (2020) (4)
Ellipsoid-based parametric estimation in the linear multidimensional systems with uncertain model description (2007) (4)
Minimization of Overshoot in Linear Discrete-Time Systems via Low-Order Controllers (2001) (4)
Hit-and-Run: randomized technique for control problems recasted as concave programming (2011) (3)
A new approach to robustness and stabilization of control systems via perturbation theory (1999) (3)
SUPERSTABLE CONTROL SYSTEMS (2002) (3)
Robust stabilization via Hit-and-Run techniques (2009) (3)
The randomized algorithm for finding an eigenvector of the stochastic matrix with application to PageRank (2009) (3)
Static Controller Synthesis for Peak-to-Peak Gain Minimization as an Optimization Problem (2021) (2)
Quadratic image of a ball: Towards efficient description of the boundary (2014) (2)
Filtering with nonrandom noise: invariant ellipsoids technique (2008) (2)
Newton Method with Adaptive Step-Size for UnderDetermined Systems of Equations (2017) (2)
Methods for solving constrained extremum problems in the presence of random noise (1979) (2)
Geometry of the stability domain in the parameter space: D-decomposition technique (2005) (2)
Filtering under nonrandom disturbances: the method of invariant ellipsoids (2008) (2)
Stability study of a power system with unipolar electromagnetic brake (2016) (2)
Stability of linear difference equations with unmodelled higher order terms (1998) (2)
Stopping Rules for Gradient Methods for Non-Convex Problems with Additive Noise in Gradient (2022) (2)
Linear Matrix Inequalities in Control Systems with Uncertainty (2021) (2)
Geometry of quadratic maps via convex relaxation (2018) (2)
Interval technique for parameter estimation under model uncertainty (2005) (2)
A PROBABILISTIC APPROACH TO ROBUST STABILITY OF TIME DELAY SYSTEMS (1996) (2)
Ellipsoidal Bounding Techniques for Parameter Tracking (1997) (2)
RACT : Randomized Algorithms Control Toolbox for MATLAB 1 (2008) (1)
Robust stability and design of linear discrete-time SISO systems under l/sub 1/ uncertainties (1997) (1)
Minimization of composite regression functions (1978) (1)
ITERATIONS OF PERTURBED TENT MAPS WITH APPLICATIONS TO CHAOS CONTROL (2006) (1)
On the strict- and wide-sense stability robustness of uncertain systems: application of a new frequency criterion (1994) (1)
Use of Projective Coordinate Descent in the Fekete Problem (2020) (1)
Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points (2019) (1)
Robustness Radius for Sector Stability of Polynomials (1996) (1)
Observer-Aided Output Feedback Synthesis as an Optimization Problem (2022) (1)
Solutions of Stable Difference Equations Probably Experience Peak (2020) (1)
OPTIMAL CONTROL OF A MECHANICAL TWO-MASS-SPRING SYSTEMUSING INVARIANT ELLIPSOIDS TECHNIQUE (2007) (1)
Robust gain margin for a cascade of uncertain links (1995) (1)
Positive realness and coprime factor uncertainty conditions for reduction of robust stabilization problems to classical H/sup /spl infin// problems (1994) (1)
Large deviations in linear control systems with nonzero initial conditions (2015) (1)
Observer-Aided Output Feedback Synthesis as an Optimization Problem (2022) (0)
Fifteenth International IFAC Congress (2003) (0)
Sparse feedback in linear control systems (2014) (0)
Centennary of Yakov Zalmanovich Tsypkin's Birth (2020) (0)
Discussion on: 'Multiobjective L1/H∞ Controller Design for Systems with Frequency and Time Domain Constraints' (2000) (0)
Using Predictive Control to Synchronize Chaotic Systems (2005) (0)
Output Feedback Controllers Synthesis with Practical Pole Clustering for Descriptor Systems (2006) (0)
He was a lucky person… (2001) (0)
First traditional Russian youth summer school “Control, information, and optimization” (2009) (0)
Sparse solutions of optimal control via Newton method for under-determined systems (2019) (0)
GUARANTIES FOR l 1 RECOVERY OF BLOCK-SPARSE SIGNALS By (2022) (0)
Stability and Performance of Complex Systems Affected by Parametric Uncertainty (2019) (0)
Principle component analysis: Robust versions (2017) (0)
Necessary and Sufficient Conditions for Robust Stability of Linear Systems with MultMYine Uncertainty Structum (1995) (0)
Stability and synchronization of oscillators: New Lyapunov functions (2017) (0)
BILLIARD WALK - NEW SAMPLING ALGORITHM (2009) (0)
Sparse solutions of optimal control with L1-objective * (2020) (0)
st Stability and Design of Linear Discrete-time SISO Systems U r I1 Uncertainties' (1997) (0)
Comments on "Two necessary conditions for a complex polynomial to be strictly Hurwitz and their applications in robust stability analysis" [with reply] (1994) (0)
Use of Projective Coordinate Descent in the Fekete Problem (2020) (0)
Guaranteed ellipsoidal state estimation for uncertain MIMO models (2003) (0)
Early control textbooks in Russia (Soviet Union) (2006) (0)
ACCURACY GUARANTIES FOR (cid:2) 1 RECOVERY OF BLOCK-SPARSE SIGNALS (2013) (0)
Stability study of a power system with unipolar electromagnetic brake (2016) (0)
On Stochastic Approximation with Arbitrarily Dependent Noise (1991) (0)
6TH SWEDISH-RUSSIAN CONTROL CONFERENCE (2011) (0)
New Criteria for Tuning PID Controllers (2022) (0)
Randomization in Robustness, Estimation, and Optimization (2018) (0)
Regularization-based solution of the PageRank problem for large matrices (2012) (0)
Stabilityregionsintheparameterspace: D-decompositionrevisited ? (2005) (0)
Fourth Russian-Swedish Conference on Control (2001) (0)
Robust Stability of Interval Matrices: a Stochastic Approach (1998) (0)
Selected Works of E.S. Pyatnitskii in 3 Volumes. Moscow: Fizmatlit, 2004, vol. 1; 2005, vol. 2 (2005) (0)
On existence and stability of equilibria of DC LTI circuits with constant power loads (2016) (0)
Design of dynamic controller for rejection of persistent disturbances (2011) (0)
A.S. Poznyak. Advanced Mathematical Tools for Automatic Control Engineers. Vol. I. Deterministic Systems. Elsevier, Amsterdam, 2008. 775 pp (2009) (0)
Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems? (2017) (0)
Optimal pseudogradient stochastic-optimization algorithms (1980) (0)
Variational Problems Arising in Statistics (1990) (0)
Stochastic Approach to a Class of Convex Optimization Problems (2007) (0)

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Boris T. Polyak's Academic­Influence.com Rankings

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Boris T. Polyak's Published Works

Published Works

Boris T. Polyak's AcademicInfluence.com Rankings