Search Results - "Polyak, B.T."

Cubic regularization of Newton method and its global performance by Nesterov, Yurii, Polyak, B.T.

“…In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme,…”
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Newton’s method and its use in optimization by Polyak, B.T.

“…Newton’s method is a basic tool in numerical analysis and numerous applications, including operations research and data mining. We survey the history of the…”
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Stochastic algorithms for exact and approximate feasibility of robust LMIs by Calafiore, G., Polyak, B.T.

“…In this note, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form F(x,/spl…”
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Random spherical uncertainty in estimation and robustness by Polyak, B.T., Shcherbakov, P.S.

“…A theorem is formulated that gives an exact probability distribution for a linear function of a random vector uniformly distributed over a ball in…”
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Probabilistic robust design with linear quadratic regulators by Polyak, B.T., Tempo, R.

“…In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators (LQR). We consider systems…”
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On the complete instability of interval polynomials by Dabbene, F., Polyak, B.T., Tempo, R.

“…In this paper, we study “complete instability” of interval polynomials, which is the counterpart of classical robust stability. That is, the objective is to…”
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Robust stability and design of linear discrete-time SISO systems under l/sub 1/ uncertainties by Polyak, B.T., Halpern, M.E.

“…Shows how value sets and the zero exclusion principle can be used to obtain results on the robust stability and design of controllers against a special…”
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Interval solutions for interval algebraic equations by Polyak, B.T., Nazin, S.A.

“…In the framework of interval uncertainty, a well-known classical problem in numerical analysis is considered, namely, to find “the best” interval solution for…”
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History of mathematical programming in the USSR: analyzing the phenomenon by Polyak, B.T.

“…I am not a historian; these are just reminiscences of a person involved in the development of optimization theory and methods in the former USSR. I realize…”
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Stability of linear difference equations with unmodelled higher order terms by Tsypkin, Ya.Z., Polyak, B.T.

“…Dedicated to Gerry Ladas on his sixtieth birthday. We consder the case when the tru linear difference equation may difer from the nominal one. Neither higher…”
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Optimal design for discrete-time linear systems via new performance index by Polyak, B.T., Halpern, M.E.

“…We introduce a class of linear discrete‐time systems called ‘superstable’. For the SISO case this means that the absolute value of the constant term of the…”
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Frequency domain criteria for l/sup p/-robust stability of continuous linear systems by Tsypkin, Y.Z., Polyak, B.T.

“…Necessary and sufficient criteria in the frequency domain for robust stability are given under the assumption that coefficients of a characteristic polynomial…”
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Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure by Polyak, B.T., Kogan, J.

“…This correspondence is concerned with an image f(B/sup m/) of a box B/sup m//spl sub/R/sup m/ under a multiaffine transformation f:R/sup m//spl rarr/C. The…”
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Discussion on: ‘Multiobjective L1/H∞ Controller Design for Systems with Frequency and Time Domain Constraints’ by Polyak, B.T., Haddad, W.M., Chellaboina, V., Kumar, R.

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High-Gain Robust Control by Tsypkin, Ya. Z., Polyak, B.T.

“…We consider linear time-invariant SISO systems with parametric or non-parametric uncertainty in the transfer function. It is assumed that the system is…”
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Multiplying Disks: Robust Stability of a Cascade Connection by Polyak, B.T., Vishnyakov, A.N.

“…An explicit formula for a product of n disks in the complex plane is obtained. It completes the circular arithmetic technique and yields numerous applications…”
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Robust stabilization via Hit-and-Run techniques by Polyak, B.T., Gryazina, E.N.

“…In previous works the authors proposed to use hit-and-run versions of Markov-chain Monte-Carlo algorithms for various problems of control and optimization. In…”
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A randomized cutting plane scheme with geometric convergence: Probabilistic analysis and SDP applications by Dabbene, F., Shcherbakov, P., Polyak, B.T.

“…We propose a randomized method for general convex optimization problems; namely, the minimization of a linear function over a convex body. The idea is to…”
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Comments on "Two necessary conditions for a complex polynomial to be strictly Hurwitz and their applications in robust stability analysis" [with reply] by Polyak, B.T., Tsypkin, Ya.Z., Shi, Y.Q., Yen, K.K., Chen, C.M.

“…In the original paper, Y. Q. Shi, K. K. Yen, and C. M. Chen (IEEE Trans. Automat. Contr., vol. 38, no. 1, p. 125-8, 1993) present two simple necessary…”
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Rejection of Bounded Disturbances via Invariant Ellipsoids Technique by Polyak, B.T., Nazin, A.V., Topunov, M.V., Nazin, S.A.

“…In this paper an approach based on invariant ellipsoids is applied to the problem of persistent disturbance rejection by means of static state-feedback…”
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