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Neural network training with optimal bounded ellipsoid algorithm

NEURAL COMPUTING & APPLICATIONS 2009年第6期18卷 623-631页

作者： de Jesus Rubio, Jose Yu, Wen Ferreyra, Andres UAM Azcapotzalco Dept Elect Area Instrumentac Mexico City DF Mexico Inst Politecn Nacl ESIME Azcapotzalco Secc Estudios Posgrad & Invest Mexico City DF Mexico IPN CINVESTAV Dept Automat Control Mexico City 07360 DF Mexico

Compared to normal learning algorithms, for example backpropagation, the optimal bounded ellipsoid (OBE) algorithm has some better properties, such as faster convergence, since it has a similar structure as Kalman filter. OBE has some advantages over Kalman filter training, the noise is not required to be Guassian. In this paper OBE algorithm is applied in training the weights of the feedforward neural network for nonlinear system identification. Both hidden layers and output layers can be updated. From a dynamic system point of view, such training can be useful for all neural network applications requiring real-time updating of the weights. Two simulations give the effectiveness of the suggested algorithm.

关键词： Neural networks Identification ellipsoid algorithm Stability

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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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Reducing Revenue to Welfare Maximization: Approximation algorithms and other Generalizations 13

Reducing Revenue to Welfare Maximization: Approximation Algo...

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Symposium on Discrete algorithms

作者： Yang Cai Constantinos Daskalakis S. Matthew Weinberg EECS MIT

ISBN: (纸本)9781611972511

It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly combinatorial) demand constraints. This reduction provides a poly-time solution to the optimal mechanism design problem in all auction settings where welfare optimization can be solved efficiently, but it is fragile to approximation and cannot provide solutions to settings where welfare maximization can only be tractably approximated. In this paper, we extend the reduction to accommodate approximation algorithms, providing an approximation preserving reduction from (truthful) revenue maximization to (not necessarily truthful) welfare maximization. The mechanisms output by our reduction choose allocations via blackbox calls to welfare approximation on randomly selected inputs, thereby generalizing also our earlier structural results on optimal multi-dimensional mechanisms to approximately optimal mechanisms. Unlike [12], our results here are obtained through novel uses of the ellipsoid algorithm and other optimization techniques over non-convex regions.

关键词： Welfare Maximization settings where welfare 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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Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model

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MATHEMATICS OF OPERATIONS RESEARCH 2009年第4期34卷 869-879页

作者： Freund, Robert M. Vera, Jorge R. MIT Alfred P Sloan Sch Management Cambridge MA 02142 USA Pontificia Univ Catolica Chile Dept Ingn Ind & Sistemas Fac Ingn Santiago 7820436 Chile

Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation oracle with no further information (e. g., no domain ball containing or intersecting the set, etc.). The authors' interest in this problem stems from fundamental issues involving the interplay of (i) the computational complexity of computing a point in the set, (ii) the geometry of the set, and (iii) the stability or conditioning of the set under perturbation. Under suitable definitions of these terms, the authors show herein that problem instances with favorable geometry have favorable computational complexity, validating conventional wisdom. The authors also show a converse of this implication by showing that there exist problem instances that require more computational effort to solve in certain families characterized by unfavorable geometry. This in turn leads, under certain assumptions, to a form of equivalence among computational complexity, geometry, and the conditioning of the set. The authors' measures of the geometry, relative to a given reference point, are based on the radius of a certain domain ball whose intersection with the set contains a certain inscribed ball. The geometry of the set is then measured by the radius of the domain ball, the radius of the inscribed ball, and the ratio between these two radii, the latter of which is called the aspect ratio. The aspect ratio arises in the analysis of many algorithms for convex problems, and its importance in convex algorithm analysis has been well-known for several decades. However, the presence in our bound of terms involving only the radius of the domain ball and only the radius of the inscribed ball are a bit counterintuitive;nevertheless, we show that the computational complexity must involve these terms in addition to the aspect ratio, even when the aspect ratio itself is small. This lower-bound complexity analysis relies on simple features of the separation oracle model;if we instead assume

关键词： convex optimization ellipsoid algorithm computational complexity

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Unfalsified model reference adaptive control using the ellipsoid algorithm

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2004年第8期18卷 683-696页

作者： Cabral, FB Safonov, MG Univ Estadual Rio Grande do Sul BR-92500000 Guaiba RS Brazil Univ So Calif Los Angeles CA 90089 USA

The unfalsified control paradigm which uses as plant information, experimental trajectories of plant signals, is applied to the model reference adaptive control problem. The use of an ellipsoid algorithm overcomes the need of gridding the parameter space used in prior applications of unfalsified control. The application of the ellipsoid algorithm produces a sequence of decreasing volume ellipsoids which contains the set of unfalsified candidates. Simulation results are provided for the control of an unstable plant. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： unfalsified control model reference adaptive control ellipsoid algorithm

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Active set strategies in an ellipsoid algorithm for nonlinear programming

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COMPUTERS & OPERATIONS RESEARCH 2004年第6期31卷 941-962页

作者： Rugenstein, EK Kupferschmid, M US Mil Acad Dept Math Sci W Point NY 10996 USA Rensselaer Polytech Inst Troy NY 12180 USA

The classical ellipsoid algorithm solves convex nonlinear programming problems having feasible sets of full dimension. Convergence is certain only for the convex case (Math. Oper. Res. 10 (1985) 515), but the algorithm often works in practice for nonconvex problems as well (SIAM J. Control Optim. 23 (1985) 657). Shah's algorithm (Comput. Oper. Res. 20 (2001) 85) modifies the classical method to permit the solution of nonlinear programs including equality constraints. This paper describes a robust restarting procedure for Shah's algorithm and investigates two active set strategies to improve computational efficiency. Experimental results are presented to show the new algorithm is effective, and usually faster than Shah's algorithm, for a wide variety of convex and nonconvex nonlinear programs with inequality and equality constraints. We also demonstrate that the algorithm can be used to solve systems of nonlinear equations and inequalities, including Karush-Kuhn-Tucker conditions.

关键词： nonlinear optimization ellipsoid algorithm equality constraints restarting strategy active set strategy computational experiments performance profiles

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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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An ellipsoid algorithm for probabilistic robust controller design

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SYSTEMS & CONTROL LETTERS 2003年第5期49卷 365-375页

作者： Kanev, S De Schutter, B Verhaegen, M Univ Twente Fac Appl Phys Syst & Control Engn Grp NL-7500 AE Enschede Netherlands Delft Univ Technol Fac Informat Technol & Syst Control Syst Engn Grp NL-2600 GA Delft Netherlands

In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a H-2 robust state-feedback controller is designed. (C) 2003 Elsevier B.V. All rights reserved.

关键词： probabilistic design randomized algorithms robust LMIs robust control ellipsoid algorithm

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An ellipsoid algorithm for equality-constrained nonlinear programs

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COMPUTERS & OPERATIONS RESEARCH 2001年第1期28卷 85-92页

作者： Shah, S Mitchell, JE Kupferschmid, M Rensselaer Polytech Inst Acad Comp Serv Troy NY 12180 USA United Airlines Elk Grove Village IL 60007 USA

This paper describes an ellipsoid algorithm that solves convex problems having linear equality constraints with or without inequality constraints. Experimental results show that the new method is also effective for so... 详细信息

关键词： nonlinear optimization ellipsoid algorithm equality constraints

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