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Convergence analysis of central and minimax algorithms in scalar regressor models

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 2006年第1期18卷 66-99页

作者： Akçay, H At, N Anadolu Univ Dept Elect & Elect Engn TR-26470 Eskisehir Turkey

In this paper, the estimation of a scalar parameter is considered with given lower and upper bounds of the scalar regressor. We derive non-asymptotic, lower and upper bounds on the convergence rates of the parameter estimate variances of the central and the minimax algorithms for noise probability density functions characterized by a thin tail distribution. This presents an extension of the previous work for constant scalar regressors to arbitrary scalar regressors with magnitude constraints. We expect our results to stimulate further research interests in the statistical analysis of these set-based estimators when the unknown parameter is multi-dimensional and the probability distribution function of the noise is more general than the present setup.

关键词： system identification membership-set central algorithm minimax algorithm Chebyshev center parameter estimate variance convergence analysis

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Ljusternik-Schnirelman minimax algorithms and an Application for Finding Multiple Negative Energy Solutions of Semilinear Elliptic Dirichlet Problem Involving Concave and Convex Nonlinearities: Part I. algorithms and Convergence

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JOURNAL OF SCIENTIFIC COMPUTING 2016年第1期66卷 19-40页

作者： Yao, Xudong Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China

In this paper, two minimax algorithms for capturing multiple saddle points are developed from well-known Ljusternik-Schnirelman critical point theory. Mathematical justification for these algorithms is established. Numerical experiment is carried out to calculate multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. Global sequence convergence result is verified.

关键词： Ljusternik-Schnirelman critical point theory Ljusternik-Schnirelman minimax algorithm Semilinear elliptic equation Concave and convex nonlinearities Finite element method Convergence

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CONVERGENCE ANALYSIS OF CENTRAL AND minimax algorithmS IN SCALAR REGRESSOR MODELS

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IFAC Proceedings Volumes 2006年第1期39卷 594-599页

作者： Hüseyin Akçay Nuray At Department of Electrical and Electronics Engineering Anadolu University 26470 Eskisehir Turkey

In this paper, estimation of a scalar parameter is considered with given lower and upper bounds of the scalar regressor. We derive non-asymptotic, lower and upper bounds on the convergence rates of the parameter estimate variances for noise probability density functions charecterized by a thin tail distribution. This presents an extension of the previous work for constant scalar regressors to arbitrary scalar regressors with magnitude constraints. We expect our results to stimulate further research interests in the statistical analysis of these set-based estimators when the unknown parameter is multi-dimensional and the probability distribution function of the noise is more general than the present setup.

关键词： System identification Membership set Central algorithm minimax algorithm Chebyshev center Parameter estimate variance Convergence analysis

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Consolidation of a WSN and minimax Method to Rapidly Neutralise Intruders in Strategic Installations

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SENSORS 2012年第3期12卷 3281-3301页

作者： Conesa-Munoz, Jesus Ribeiro, Angela UPM CSIC Ctr Automat & Robot Madrid 28500 Spain

Due to the sensitive international situation caused by still-recent terrorist attacks, there is a common need to protect the safety of large spaces such as government buildings, airports and power stations. To address this problem, developments in several research fields, such as video and cognitive audio, decision support systems, human interface, computer architecture, communications networks and communications security, should be integrated with the goal of achieving advanced security systems capable of checking all of the specified requirements and spanning the gap that presently exists in the current market. This paper describes the implementation of a decision system for crisis management in infrastructural building security. Specifically, it describes the implementation of a decision system in the management of building intrusions. The positions of the unidentified persons are reported with the help of a Wireless Sensor Network (WSN). The goal is to achieve an intelligent system capable of making the best decision in real time in order to quickly neutralise one or more intruders who threaten strategic installations. It is assumed that the intruders' behaviour is inferred through sequences of sensors' activations and their fusion. This article presents a general approach to selecting the optimum operation from the available neutralisation strategies based on a minimax algorithm. The distances among different scenario elements will be used to measure the risk of the scene, so a path planning technique will be integrated in order to attain a good performance. Different actions to be executed over the elements of the scene such as moving a guard, blocking a door or turning on an alarm will be used to neutralise the crisis. This set of actions executed to stop the crisis is known as the neutralisation strategy. Finally, the system has been tested in simulations of real situations, and the results have been evaluated according to the final state of the intruders. I

关键词： intelligent systems wireless sensor network decision support systems minimax algorithm path planning risk measure surveillance system

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Can modified minimax win in Pearl's game?

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2018年第Nov.期57卷 23-27页

作者： Cai, Haoyang Ma, Haodong Li, Linyu Zhang, Luming Hangzhou Foreign Languages Sch 12 Grade Hangzhou Zhejiang Peoples R China Zhengzhou Foreign Languages Sch 12 Grade Zhengzhou Henan Peoples R China Bishop Hendricken High Sch 12 Grade Warwick RI USA Zhejiang Univ Coll Comp Sci Hangzhou Zhejiang Peoples R China

minimax algorithm is widely used for adversarial searching. It is commonly believed that searching depth and winning chance has a positive correlation, but Dana S. Nau pointed out in his 1982 research that in Pearl's game, pathology occurs. minimax shows a decrease of winning chance as searching depth increases. Our research proposes a possible way to fix the pathology by taking the opponent's strategy into consideration in some specific cases. The experiment proves that the accumulation of incorrect predictions at least partially causes the pathology. Our modified version of minimax successfully overcomes the pathology and continues to present the power of minimax in Pearl's game. (C) 2018 Elsevier Inc. All rights reserved.

关键词： minimax algorithm Modified minimax algorithm Pearl's game

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minimax Checkers Playing GUI: A Foundation for AI Applications 25

Minimax Checkers Playing GUI: A Foundation for AI Applicatio...

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25th IEEE International Conference on Electronics, Electrical Engineering and Computing (INTERCON)

作者： Escandon, Elmer R. Campion, Joseph Univ Ingn & Tecnol UTEC Dept Elect & Mechatron Engn Lima Peru

ISBN: (纸本)9781538654903

This paper presents an application that uses artificial intelligence (AI) to play checkers. The program application has a MATLAB graphical user interface (GUI) and is equipped with a minimax algorithm. The AI has proven to be successful against the average student at the Universidad de Ingenier ' ia y Tecnologia (UTEC) in a game of checkers. The importance of this project resides in providing the first steps at research and implementation of artificial intelligence that could be used in applications such as robotics in manufacturing and project planning. The project accomplished the objectives of creating an AI GUI that could play checkers against UTEC students. As was expected, success of the AI depended on the depth of the minimax tree. The AI struggled against UTEC students while using tree depths of three and four levels;however, the AI proved successful against UTEC students at tree depths of five and six. The optimal level chosen for the checkers AI eventually was five levels of depth because for six or more levels, the time of minimax evaluation delayed too much for fluid human game play.

关键词： AI Foundations minimax algorithm Artificial intelligence Graphical User Interface

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Combining imperfect components (III) - minimax optimization of multidimensional cost error

Combining imperfect components (III) - Minimax optimization ...

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International Conference on Parallel and Distributed Processing Techniques and Applications

作者： Kamura, Y Nakamori, M Tokyo A&T Univ Dept Comp Informat & Commun Sci Tokyo 1848588 Japan

ISBN: (纸本)1932415262

We consider the problem of optimally combining individual lenses for the lens systems used in semiconductor exposure equipment. Given a lens system with m lenses A(1), A(2), . . . ,A(m), then for n lens systems we need n individual lenses for each A(i). Our objective is to combine the n individual lenses in such a way that the maximum aberration occurring in any of the n combinations is minimized. We formulate the problem as a modified assignment problem with a vector cost and a minimax objective function. A new algorithm of polynomial time is proposed and the results from numerical experiments are presented.

关键词： assignment problem minimax algorithm optimal combination

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minimax Guided Reinforcement Learning for Turn-based Strategy Games 2

Minimax Guided Reinforcement Learning for Turn-based Strateg...

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2nd International Conference on Information and Communication Technology (ICoICT)

作者： Santoso, Sulaeman Supriana, Iping Bandung Inst Technol Sch Elect Engn & Informat Bandung Indonesia

ISBN: (纸本)9781479935802

Games are a good medium for artificial intelligence ( AI) research, since they compare user and machine behavior directly. AI in games is required to imitate human behavior. Though nowadays the use of rule base scripting and hard code behavior is still dominant in commercial game, the use of learning algorithm can be an alternative because of its ability to adapt to changes and to achieve substantial result at a moderate time. This paper investigates the use of learning which is derived from dynamic scripting to provide action in a turn-based strategy game. The algorithm is then combined with the minimax algorithm to achieve a better performance. The performance of the proposed algorithm is evaluated through a series of matches against a static manually designed AI. The result shows that the proposed algorithm is able to adapt the static AI at a shallow minimax depth. The algorithm also shows the ability reducing calculation time and using less memory space. It is concluded that minimax guided reinforcement learning can be applied to the turn based strategy genre.

关键词： Artificial intelligence reinforcement learning minimax algorithm turn-based strategy

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A GLOBAL ROUTER BASED ON A MULTICOMMODITY FLOW MODEL

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INTEGRATION-THE VLSI JOURNAL 1987年第1期5卷 3-16页

作者： SHRAGOWITZ, E KEEL, S CONTROL DATA CORP DEPT ADV CADMINNEAPOLISMN 55440 UNIV CHICAGO DEPT MATHCHICAGOIL 60637

The paper describes a new global router applicable for any object with a defined channel structure. This router can be used for the routing of chips and boards with rectilinear or nonrectilinear channel topology in a multilayer environment. This makes it more universal than other known global routers. The router is based on a multicommodity flow model in the graph form with hierarchical cost function. This model is proved to be NP-complete. An algorithm applied to this problem is based on minimax ideas. It moves from the solution optimal w/r to an initial cost function in the direction of the constraints by maximizing on each iteration the decrease in the number of channels at the highest level of overflow and the number of cells with overflown via count. If a solution exists for each iteration, then algorithm will converge in polynomially bounded number of steps to the solution of the multicommodity flow problem. If, for some iteration, a solution does not exist, then an escape procedure is applied and the process continues. Experimental results indicate that performance characteristics of this global router are not inferior to global routers applicable only to gate arrays.

关键词： Global router multicommodity flow problem graph model minimax algorithm hierarchical objective function

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Minimization of the maximum error signal in active control

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 1998年第3期6卷 268-281页

作者： Gonzalez, A Albiol, A Elliott, SJ Univ Politecn Valencia Dept Comunicac E-46071 Valencia Spain

The purpose of this paper is to present a new multichannel adaptive filtering algorithm for the active control of single frequency noise in acoustic systems. Most active control systems with multiple error sensors minimize the sum of the modulus squared output of these sensors. In this study, an adaptive algorithm is presented that minimizes an alternative cost function which, in the limit, is equal to the maximum of the modulus squared values of all the error sensors. The physical consequences are investigated of minimizing the maximum modulus squared output to achieve noise reductions are investigated. An analytical framework is developed that covers steady state performance as well as convergence properties. By means of simulations, the proposed algorithm has been applied to a linear model of a one-dimensional (1-D) acoustic system and compared with the classical least squares solutions. The proposed algorithm is also used in simulations of the control of the pressure measured at 32 microphone positions in a room using 16 loudspeakers, when the room is excited with an 88 Hz pure tone. The results of these simulations show that the observed convergence and steady-state properties agree well with the theoretical predictions. A comparison with the least squares solutions leads to the conclusion that the proposed algorithm leads to a more uniform acoustic field in the enclosure than the classical least squares algorithm.

关键词： active noise control minimax algorithm steepest descent algorithm

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