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Recursive Set-Membership Parameter Estimation Using Fractional Model

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2015年第12期34卷 3757-3788页

作者： Amairi, M. Univ Gabes Natl Engn Sch Gabes ENIG Res Unit Modeling Anal & Control Syst MACS UR 06 Gabes 6029 Tunisia

This paper deals with time-domain set-membership parameter estimation using fractional model in case of unknown-but-bounded equation error with a priori known noise bounds. In such bounded-error context, the main goal is to characterize the set of all feasible parameters compatible with the model, the measured data and some prior error bounds. The characterization is done using the outer bounding ellipsoid strategy adapted for fractional system parameters estimation. To ensure good convergence of the used algorithms, several procedures for the selection of the more suitable excitation signal and for the equation-error bound computation are proposed and discussed. When the system is commensurate, an iterative algorithm is proposed to deal with commensurate order estimation. The performances of the proposed schemes are illustrated by a numerical example via Monte Carlo simulations and through a real application of the proposed set-membership identification method on an electronic system.

关键词： Bounded error ellipsoid algorithm Fractional calculus Parameter estimation Set-membership

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Efficient Localization Methods for Passivity Enforcement of Linear Dynamical Models

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2014年第9期33卷 1328-1341页

作者： Mahmood, Zohaib Grivet-Talocia, Stefano Chinea, Alessandro Calafiore, Giuseppe C. Daniel, Luca MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA Politecn Torino Dept Elect I-10129 Turin Italy IdemWorks Srl I-10129 Turin Italy Politecn Torino Dept Control & Comp Engn I-10129 Turin Italy

This paper describes a novel approach for passivity enforcement of compact dynamical models of electrical interconnects. The proposed approach is based on a parameterization of general state-space scattering models with fixed poles. We formulate the passivity constraints as a unitary boundedness condition on the H-infinity norm of the system transfer function. When this condition is not verified, we use it as an explicit constraint within an iterative perturbation loop of the system state-space matrices. Since the resulting optimization framework is convex but non-smooth, we solve it via localization based algorithms, such as the ellipsoid and the cutting plane methods. The proposed technique solves two critical bottleneck issues of the existing approaches for passivity enforcement of linear macromodels. Compared to quasi-optimal schemes based on singular value or Hamiltonian eigenvalue perturbation, we are able to guarantee convergence to the optimal solution. Compared to convex formulations based on direct Bounded Real Lemma constraints, we are able to reduce both memory and time requirements by orders of magnitude. We demonstrate the effectiveness of our approach on a number of cases for which existing algorithms either fail or exhibit very slow convergence.

关键词： Convex optimization cutting plane method ellipsoid algorithm localization methods passive macromodeling

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Linear Precoding Design for Mutual Information Maximization in Generalized Spatial Modulation With Finite Alphabet Inputs

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IEEE COMMUNICATIONS LETTERS 2015年第8期19卷 1323-1326页

作者： Jin, Seung-Ri Choi, Won-Chul Park, Jung-Hyun Park, Dong-Jo Korea Adv Inst Sci & Technol Dept Elect Engn Taejon 305701 South Korea Samsung Elect Co Ltd Suwon 443742 South Korea

In this letter, we develop a new precoding scheme that improves the performance of mutual information for generalized spatial modulation (GSM). First, the closed-form expression of the mutual information of the GSM with finite alphabet inputs is derived in order to update the precoder with regard to the mutual information. The joint precoding design problem to maximize the mutual information of the GSM is difficult to solve directly since it is a non-convex coupled problem. In order to solve this problem, we transform the GSM system into a virtual multiple-input multiple-output (MIMO) system, and then an extended ellipsoid algorithm is applied. Each precoder of the GSM can be solved using the common precoder of the virtual MIMO. The numerical results demonstrate that the proposed precoding scheme significantly enhances the performance in terms of the mutual information.

关键词： Generalized spatial modulation (GSM) finite alphabet inputs mutual information precoding ellipsoid algorithm

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FUZZY-PROGRAMMING TECHNIQUE TO SOLVE MULTIOBJECTIVE GEOMETRIC-PROGRAMMING PROBLEMS

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FUZZY SETS AND SYSTEMS 1992年第1期51卷 67-71页

作者： BISWAL, MP Department of Mathematics Indian Institute of Technology Kharagpur India

In this paper fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programm... 详细信息

关键词： FUZZY PROGRAMMING GEOMETRIC PROGRAMMING VECTOR-MINIMUM AND VECTOR-MAXIMUM PROBLEM ellipsoid algorithm

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A note on two fixed point problems

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JOURNAL OF COMPLEXITY 2007年第4-6期23卷 952-961页

作者： Boonyasiriwat, Ch. Sikorski, K. Xiong, Ch. Univ Utah Sch Comp Salt Lake City UT 84112 USA Univ Utah Dept Chem Salt Lake City UT 84112 USA

We extend the applicability of the Exterior ellipsoid algorithm for approximating n-dimensional fixed points of directionally nonexpanding functions. Such functions model many practical problems that cannot be formulated in the smaller class of globally nonexpanding functions. The upper bound 2n(2) ln(2/epsilon) on the number of function evaluations for finding epsilon-residual approximations to the fixed points remains the same for the larger class. We also present a modified version of a hybrid bisection-secant method for efficient approximation of univariate fixed point problems in combustion chemistry. (c) 2007 Elsevier Inc. All rights reserved.

关键词： fixed point problems optimal algorithms nonlinear equations ellipsoid algorithm computational complexity

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COMPARISON OF A SPECIAL-PURPOSE algorithm WITH GENERAL-PURPOSE algorithmS FOR SOLVING GEOMETRIC-PROGRAMMING PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第2期43卷 237-263页

作者： ECKER, JG KUPFERSCHMID, M SACHER, RS RENSSELAER POLYTECH INST OPERAT RES & STAT PROGRAMTROYNY 12181 VOORHEES COMP CTR TROYNY

We study the performance of four general-purpose nonlinear programming algorithms and one special-purpose geometric programming algorithm when used to solve geometric programming problems. Experiments are reported which show that the special-purpose algorithm GGP often finds approximate solutions more quickly than the general-purpose algorithm GRG2, but is usually not significantly more efficient than GRG2 when greater accuracy is required. However, for some of the most difficult test problems attempted, GGP was dramatically superior to all of the other algorithms. The other algorithms are usually not as efficient as GGP or GRG2. The ellipsoid algorithm is most robust.

关键词： Geometric programming computational comparisons nonlinear programming ellipsoid algorithm generalized reduced gradient algorithm

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The optimal power distribution in cooperative communication relay system

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High Technology Letters 2013年第4期19卷 371-377页

作者：张超一 Wu Muqing Miao Jiansong Luan Linlin Laboratory of Network System Architecture and Convergence Beijing University of Post and Telecommunications College of Technology Beijing Forestry University

In order to optimize power utilization of relay nodes in cooperative communication,a power allocation algorithm with objective function to maximize system capacity is *** on the convex optimization theory,an ellipsoid algorithm is used to solve this problem,which could simplify the subgradient choosing steps and improve convergence stability,so that an optimized power allocation algorithm is *** analysis and simulation results show that the algorithm can effectively distribute the power of each node with lower complexity,and ensure the transmission capability of relay nodes in cooperative communication.

关键词： relay network power distribution convex optimization ellipsoid algorithm

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Iterant recombination with one-norm minimization for multilevel Markov chain algorithms via the ellipsoid method

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COMPUTING AND VISUALIZATION IN SCIENCE 2011年第2期14卷 51-65页

作者： De Sterck, Hans Miller, Killian Sanders, Geoffrey Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94551 USA

Recently, it was shown how the convergence of a class of multigrid methods for computing the stationary distribution of sparse, irreducible Markov chains can be accelerated by the addition of an outer iteration based on iterant recombination. The acceleration was performed by selecting a linear combination of previous fine-level iterateswith probability constraints to minimize the two-norm of the residual using a quadratic programming method. In this paper we investigate the alternative of minimizing the one-norm of the residual. This gives rise to a nonlinear convex program which must be solved at each acceleration step. To solve this minimization problem we propose to use a deep-cuts ellipsoid method for nonlinear convex programs. The main purpose of this paper is to investigate whether an iterant recombination approach can be obtained in this way that is competitive in terms of execution time and robustness. We derive formulas for subgradients of the one-norm objective function and the constraint functions, and show how an initial ellipsoid can be constructed that is guaranteed to contain the exact solution and give conditions for its existence. We also investigate using the ellipsoid method to minimize the two-norm. Numerical tests show that the one-norm and twonorm acceleration procedures yield a similar reduction in the number of multigrid cycles. The tests also indicate that onenorm ellipsoid acceleration is competitive with two-norm quadratic programming acceleration in terms of running time with improved robustness.

关键词： Markov chain Iterant recombination ellipsoid algorithm Multigrid Convex programming

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Achieving target equilibria in network routing games without knowing the latency functions

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GAMES AND ECONOMIC BEHAVIOR 2019年第0期118卷 533-569页

作者： Bhaskar, Umang Ligett, Katrina Schulman, Leonard J. Swamy, Chaitanya Tata Inst Fundamental Res Sch Technol & Comp Sci Mumbai Maharashtra India CALTECH Dept Comp & Math Sci Pasadena CA 91125 USA Hebrew Univ Jerusalem Benin Sch Comp Sci & Engn Jerusalem Israel Univ Waterloo Dept Combinator & Optimizat Waterloo ON Canada Univ Calif Berkeley Simons Inst Theory Comp Berkeley CA USA

The analysis of network routing games typically assumes precise, detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as an equilibrium. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. We give a crisp positive answer to this question. We show that one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes tolls as input and outputs the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and extends to various other settings. We obtain improved query-complexity bounds for series-parallel networks, and single-commodity routing games with linear latency functions. Our techniques provide new insights into network routing games. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Routing games Network flows Tolls Stackelberg routing Query complexity ellipsoid algorithm

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Complexity of linear programming

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Operations Research Letters 1982年第2期1卷 59-62页

作者： Traub, J.F. Woźniakowski, H. Department of Computer Science Columbia University New York NY 10027 United States Institute of Informatics University of Warsaw Warsaw Poland Department of Computer Science Columbia University New York NY 10027 United States

The complexity of linear programming is discussed in the "integer" and "real number" models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation. Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all "reasonable" models of computation. © 1982.

关键词： Computational complexity ellipsoid algorithm linear inequalities linear programming models of computation polynomial-time algorithm

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