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EXTENSION OF smoothing NEWTON algorithmS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES

Journal of Systems Science & Complexity 2011年第1期24卷 195-206页

作者： Zhenghai HUANG Xiaohong LIU Department of Mathematics School of Science Tianjin University Tianjin 300072 China

There recently has been much interest in studying some optimization problems over symmetric cones. This paper deals with linear programming over symmetric cones （SCLP）. The objective here is to extend the Qi-Sun-Zhou＇s smoothing Newton algorithm to solve SCLP, where characterization of symmetric cones using Jordan algebras forms the fundamental basis for our analysis. By using the theory of Euclidean Jordan algebras, the authors show that the algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results for solving the second-order cone programming are also reported.

关键词： Euclidean Jordan algebra linear programming smoothing algorithm symmetric cone.

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Variable structure multiple model fixed-interval smoothing

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Chinese Journal of Aeronautics 2023年第2期36卷 139-148页

作者： Bolun ZHANG Yongxin GAO Zhansheng DUAN Faculty of Electronic and Information Engineering School of Automation Science and EngineeringXi’an Jiaotong UniversityXi'an 710049China

This paper focuses on fixed-interval smoothing for stochastic hybrid *** the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are *** develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this *** propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation *** improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)*** turns out that the smoothing performance is further improved by the LMS due to less competition among *** results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.

关键词： Fixed-interval smoothing Model-set adaptation Multiple model estimation smoothing algorithm Variable structure

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ADAPTIVE smoothing OF SPECTROSCOPIC DATA BY A LINEAR MEAN-SQUARE ESTIMATION

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APPLIED SPECTROSCOPY 1984年第1期38卷 49-58页

作者： KAWATA, S MINAMI, S Department of Applied Physics Osaka University Suita Osaka 565 Japan

An adaptive smoothing method based on a least mean-square estimation is developed for noise filtering of spectroscopic data. The algorithm of this method is nonrecursive and shift-varying with the local statistics of data. The mean and the variance of the observed spectrum at an individual sampled point are calculated point by point from its local mean and variance. By this method, in the resultant spectrum, the signal-to-noise ratio is maximized at any local section of the entire spectrum. Experimental results for the absorption spectrum of ammonia gas demonstrate that this method distorts less amount of signal components than the conventional smoothing method based on the polynomial curve-fitting and suppresses noise components satisfactorily. The computation time of this algorithm is rather shorter than that of the convolution algorithm with seven weighting coefficients. The a priori information for the estimation of the signal by this method are: the variance of noise, which can be attainable in the experiment; and the window function which gives the local statistics. The investigation of various types of window functions shows that the selection of the window function does not directly affect the performance of adaptive smoothing.

关键词： smoothing algorithm Data processing Computer applications

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smoothing techniques in solving non-Lipschitz absolute value equations

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2023年第4期100卷 867-879页

作者： Yilmaz, Nurullah Sahiner, Ahmet Suleyman Demirel Univ Dept Math Isparta Turkiye

In this study, we define for the first time the non-Lipschitz generalization of absolute value equations and concentrate on solving the problem of non-Lipschitz absolute value equations based on smoothing techniques. Two different types of smoothing techniques which are local and global ones are considered in smoothing process of the problem. With the help of these smoothing techniques, the non-Lipschitz absolute value equations are reformulated as a family of parametrized smooth equations. Two new algorithms are developed to solve the problem by the help of smoothing functions. Finally, the numerical experiments have been performed to illustrate the efficiency of the new algorithms.

关键词： smoothing techniques smoothing algorithm absolute value equations non-Lipschitz functions Newton algorithm

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Flight Control Design using Incremental Nonlinear Dynamic Inversion with Fixed-lag smoothing Estimation

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INTERNATIONAL JOURNAL OF AERONAUTICAL AND SPACE SCIENCES 2020年第4期21卷 1047-1058页

作者： Cervantes, Tito J. Ludena Choi, Seong H. Kim, Byoung S. Gyeongsang Natl Univ Aerosp Dept Jinju 52828 Gyeongsangnam D South Korea

In this study, a flight control design strategy based on incremental nonlinear dynamic inversion (INDI) and smoothing algorithm is presented. The INDI is an enhanced version of the nonlinear dynamic inversion technique with a better robust performance. It reduces the aircraft model dependence via the feedback information of the state derivative, that is, angular acceleration for the aircraft attitude motion (or angular velocity related to the wind axis parameters). However, the state derivatives cannot always be obtained by direct measurement, thus they need to be estimated on-line. Moreover, taking into account that INDI requires one-step delay of state derivative and the fact that the inertial measurement unit (IMU) operates faster than the flight control computer (FCC), there will be additional information that can be used to improve the estimation. Therefore, a fixed-lag smoothing algorithm based on a discrete Kalman filter is proposed for angular velocity and angular acceleration estimation. The smoother utilizes the state variable from the sensor measurement and thus dealing with noise and delay.

关键词： Incremental nonlinear dynamic inversion smoothing algorithm Control augmentation system

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A smoothing Newton method for symmetric cone complementarity problems

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OPTIMIZATION LETTERS 2015年第2期9卷 225-244页

作者： Tang, Jia Ma, Changfeng Fujian Normal Univ Dept Math & Comp Sci Fuzhou 350007 Peoples R China

Recently, there has been much interest in studying optimization problems over symmetric cones. This paper uses Euclidean Jordan algebras as a basic tool to construct a new smoothing function for symmetric cone complementarity problems. It is showed that this new function has similar structure and some good properties as the widely used symmetric perturbed Chen-Harker-Kanzow-Smale smooth function. In particularly, based on the function, we obtain global convergence and locally superlinear convergence of the smoothing Newton algorithm under two weaker assumptions respectively. Some numerical results for second-order cone complementarity problems are also reported.

关键词： Complementarity problem Symmetric cone Euclidean ordan algebra smoothing algorithm

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Optimization of image quality for decoded images using three-dimensional smoothing method

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APPLIED MATHEMATICS AND COMPUTATION 2001年第1-3期120卷 301-311页

作者： Shohdohji, T Hoshino, Y Nippon Inst Technol Fac Engn Dept Syst Engn Miyashiro Saitama 3458501 Japan

Joint Photographic Experts Group (JPEG) baseline algorithm is widely used because of its high compression capability. The algorithm has a characteristic that the degradation of image quality tends to be perceived as the compression ratio becomes high. The eyesore degradations are false contour and mosquito. A method of improving the image quality is proposed. The first step: a domain of false contours is extracted from the image and the second step: the domain is smoothed by a fitting process. It is confirmed that this method is effective in improving the image quality degraded by the JPEG high compression. (C) 2001 Elsevier Science Inc. All rights reserved.

关键词： JPEG DCT false contour method of least squares smoothing algorithm

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Near Optimum Low Complexity smoothing Loops for Dynamical Phase Estimation-Application to BPSK Modulated Signals

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第9期57卷 3704-3711页

作者： Yang, J. Geller, B. ENS Cachan Lab SATIE F-94235 Cachan France ENSTA ParisTech LEI F-75739 Paris France

This correspondence provides and analyzes a low complexity, near optimum, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low complexity sequential estimators, i.e., two phase-locked loops (PLLs). Based on a linear approximation of the problem, a theoretical performance evaluation is given. The theoretical results are compared to some simulation results and to the Bayesian and hybrid Cramer-Rao bounds. They illustrate the good performance of the proposed smoothing PLL (S-PLL) algorithm.

关键词： Dynamical phase estimation phase-locked loop (PLL) smoothing algorithm

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Evaluating supply chain flexibility under demand uncertainty with smoothing approach and VMI considerations

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2018年第8期35卷 486-505页

作者： Bodaghi, Gholamreza Jolai, Fariborz Rabbani, Masoud Univ Tehran Sch Ind Engn Coll Engn Tehran Iran

In this paper, we develop a four-stage procedure for evaluating and improving a supplier's volume flexibility. In the first stage, we use historical demand data to develop a model for forecasting their future quantities. In the next stage, we develop an algorithm for smoothing the forecasted future demands. We show that applying this algorithm not only reduces production fluctuations and damages, but also improves the flexibility of the supplier and hence the overall supply chain. We investigate the economical conditions of applying this algorithm. In the third stage, by considering the forecasted future demands, we develop a mathematical single-period flexibility measure. In the fourth stage, the developed measure is extended to a multi-period model for applying in the multi-period supply collaborations and especially in the VMI systems. Furthermore, we consider weight coefficients for taking into account the different importance of flexibility from the buyer's perspective over the time horizon. By applying in a real case study about an oil refinery, we verify the developed model and investigate the effects of its parameters through the sensitivity analysis.

关键词： Flexibility measure multiperiod vendor managed inventory smoothing algorithm

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Analysis of smoothing-type algorithms for the convex second-order cone programming

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2015年第1-2期48卷 173-185页

作者： Dong, Li Wang, Hongqin Xinyang Normal Univ Coll Math & Informat Sci Xinyang 464000 Peoples R China China Agr Univ Sch Technol Yantai Res Inst Yantai 264670 Peoples R China

There recently has been much interest in smoothing-type algorithms for solving the linear second-order cone programming (LSOCP). We extend such method to solve the convex second-order cone programming (CSOCP), which is an extension of the LSOCP. In this paper, we first propose a new smoothing function. Based on this function, we establish a smoothing Newton algorithm for solving the CSOCP and prove that the algorithm is globally and locally quadratically convergent under suitable assumptions. For the established algorithm, we use a generalized Armijo-type search rule to generate the step size. Some numerical results are reported which indicate the effectiveness of our algorithm.

关键词： Euclidean Jordan algebra Convex second-order cone programming smoothing algorithm Convergence

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