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Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search

Science China Mathematics 2009年第4期52卷 833-848页

作者： HUANG ZhengHai HU ShengLong HAN JiYe Department of Mathematics School of ScienceTianjin UniversityTianjin 300072China Institute of Applied Mathematics Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100080China

In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.

关键词： complementarity problem symmetric cone Euclidean Jordan algebra smoothing algorithm global convergence 90C25 90C33

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Application of a full-dimensional observable smoothing algorithm in SINS 31

Application of a full-dimensional observable smoothing algor...

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31st Chinese Control And Decision Conference (CCDC)

作者： Wang, Tiansheng Li, Qing Li, Chao Zhao, Hui Beijing Informat Sci & Technol Univ Beijing Key Lab High Dynam Nav Technol Beijing 100101 Peoples R China Beijing Informat Sci Technol Univ Inst Intelligent Control Sch Automat Beijing 100192 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

ISBN: (纸本)9781728101057

The traditional zero-velocity correction algorithm (ZUPT) can theoretically suppress the accumulation of navigation errors, but it can only correct the state errors of the zero-velocity interval and the observations are less. The state information of the model solution based on the SINS algorithm and the navigation error equation in the non-zero-velocity interval causes a sudden change in the entire pedestrian trajectory process, that is, the stability is poor and the accuracy is not high. This paper proposed a algorithm, which 3D errors of attitude and position are added as observations to achieve full-dimensional observability based on the traditional zero-velocity correction, then all state errors are obtained by EKF estimation, and a post-processing smoothing algorithm is introduced to make full use of the measurement information over the entire time period to correct the navigation errors of the non-zero-velocity interval. In order to verify the accuracy and stability of the algorithm, experiments were carried out by using the self-developed IMU. The results show that the proposed algorithm has better stability than the traditional ZUPT, improves the smoothness of the trajectory', and the navigation accuracy is improved by 1.7%.

关键词： SINS Full Dimensional Observation Extended Kalman Filter Zero Velocity Update Error observation smoothing algorithm

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IMPACT OF GNSS SIGNAL OUTAGE ON EOPS USING FORWARD KALMAN FILTER AND smoothing algorithm 24

IMPACT OF GNSS SIGNAL OUTAGE ON EOPS USING FORWARD KALMAN FI...

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24th ISPRS Congress on Imaging Today, Foreseeing Tomorrow

作者： Jouybari, Arash Bagherbandi, Mohammad Nilfouroushan, Faramarz Univ Gavle Fac Engn & Sustainable Dev Gavle Sweden Royal Inst Technol KTH Div Geodesy & Satellite Positioning Stockholm Sweden Dept Geodet Infrastruct Geodata Div Gavle Sweden

The global navigation satellite system (GNSS) has been playing the principal role in positioning applications in past decades. Position robustness degrades with a standalone receiver due to GNSS signal outage in mobile mapping systems. The GNSS and inertial measurement unit (IMU) integration is used to solve positioning degradation. This article studies the GNSS/IMU integration processing (i.e., forward Kalman filter (KF) and smoothing algorithm) using a single or a network of nearby GNSS reference stations. In addition, we analyze the impact of simulated GNSS signal outage on exterior orientation parameters (EOPs). The outcomes confirm that the smoothing algorithm works better than the forward KF and improves the accuracy for position and orientation in the case when there is no GNSS signal outage. Also, it improves the position and orientation accuracy by about 95% and 60% when there is a 180 second GNSS signal outage, respectively.

关键词： Tightly Coupled Forward Kalman Filter GNSS/IMU Integration smoothing algorithm Virtual Reference Station Exterior Orientation Parameters Differential GNSS processing

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An application of a Kalman Filter Fixed Interval smoothing algorithm to underwater target tracking

An application of a Kalman Filter Fixed Interval Smoothing A...

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作者： Richard H. Nicklas Naval Postgraduate School

学位级别：硕士

A Fortran program was developed to implement a Kalman Filter and Fixed Interval smoothing algorithm to optimally smooth data tracks generated by the short base-line tracking ranges at the Naval Torpedo Station, Keyport, Washington. The program is designed to run on a personal computer and requires as input a data file consisting of X, Y, and Z position coordinates in sequential order. Data files containing the filtered and smoothed estimates are generated by the program. This algorithm uses a second order linear model to predict a typical target's dynamics. The program listings are in- cluded as appendices. Several runs of the program were performed using actual range data as inputs. Re- sults indicate that the program effectively reduces random noise, thus providing very- smooth target tracks which closely follow the raw data. Tracks containing data gener- ated in an overlap region where one array hands off the target to the next array are highlighted. The effects of varying the magnitude of the excitation matrix Q(k) are also explored. This program is seen as a valuable post-data analysis tool for the current tracking range data. In addition, it can easily be modified to provide improved real time, on line tracking using the Kalman Filter portion of the algorithm alone.

关键词： Kalman Filter smoothing algorithm torpedo tracking

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An Improved 2D Adaptive smoothing algorithm in Image NoiseRemoval and Feature Preservation

An Improved 2D Adaptive Smoothing Algorithm in Image NoiseRe...

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作者： Hu, Xin University of Cincinnati

学位级别：master

We introduce an improved 2D adaptivesmoothing algorithm for noise removal and feature *** to the original 2D adaptive smoothing algorithm, this newalgorithm is also based on the novel idea of utilizing contextualdiscontinuity and local discontinuity jointly to detect anddistinguish edges and noise. The new algorithm improves the mainconcept?– contextual discontinuity by introducing a novelhomogeneity region definition with a corresponding method forcontextual discontinuity measurement. Comparing to the originalalgorithm and other smoothing algorithms, the improved algorithmcan preserve edges more effectively while *** improved 2D algorithm has beenimplemented and extensive experiments have been carried out tocompare the algorithm to the original algorithm and other smoothingstrategies to quantitatively demonstrate improvement inperformance. Measurements are applied to evaluate the noise removaland edge preservation performance. Simulation results show thatthis improved algorithm has a superior performance over both theoriginal algorithm and other popular smoothing strategies in noiseremoval as well as feature preservation

关键词： SNR smoothing algorithm algorithm Pixel Image iteration number

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A Collision-Free G² Continuous Path-smoothing algorithm Using Quadratic Polynomial Interpolation

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2014年第12期11卷 194-194页

作者： Chang, Seong-Ryong Huh, Uk-Youl Inha Univ Dept Elect Engn Inchon South Korea

Most path-planning algorithms are used to obtain a collision-free path without considering continuity. On the other hand, a continuous path is needed for stable movement. In this paper, the searched path was converted into a G(2) continuous path using the modified quadratic polynomial and membership function interpolation algorithm. It is simple, unique and provides a good geometric interpretation. In addition, a collision-checking and improvement algorithm is proposed. The collision-checking algorithm can check the collisions of a smoothed path. If collisions are detected, the collision improvement algorithm modifies the collision path to a collision-free path. The collision improvement algorithm uses a geometric method. This method uses the perpendicular line between a collision position and the collision piecewise linear path. The sub-waypoint is added, and the QPMI algorithm is applied again. As a result, the collision-smoothed path is converted into a collision-free smooth path without changing the continuity.

关键词： Continuous path Function approximation Interpolation Path planning Path smoothing Robot motion smoothing algorithm Smooth path Vehicle navigation

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APPLYING METRIC REGULARITY TO COMPUTE A CONDITION MEASURE OF A smoothing algorithm FOR MATRIX GAMES

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SIAM JOURNAL ON OPTIMIZATION 2010年第6期20卷 3490-3511页

作者： Mordukhovich, Boris S. Pena, Javier F. Roshchina, Vera Wayne State Univ Detroit MI 48202 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA Univ Evora Evora Portugal

We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed by Gilpin, Pena, and Sandholm [Proceedings of the 23rd Conference on Artificial Intelligence, 2008, pp. 75-82] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

关键词： matrix games smoothing algorithm condition measure variational analysis metric regularity generalized differentiation

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Calculating the grain boundary inclination of voxelated grain structures using a smoothing algorithm

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SCRIPTA MATERIALIA 2022年 218卷

作者： Yang, Lin Hilty, Floyd Muralikrishnan, Vivekanand Silva-Reyes, Kenneth Harley, Joel B. Krause, Amanda R. Tonks, Michael R. Univ Florida Dept Mat Sci & Engn Gainesville FL 32611 USA Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Pacific Northwest Natl Lab Richland WA 99354 USA

We have developed a flexible method for calculating the grain boundary (GB) inclinations of voxelated grain structure data using smoothing algorithms. We compared the performance of four algorithms: the linear interpolation, Allen-Cahn, level-set, and vertex algorithms. We assessed their accuracy using 2D and 3D cases with known inclinations. The vertex algorithm provided the best balance between accuracy and efficiency for 2D structures while the linear interpolation algorithm provided the best balance for 3D structures. We compared the GB inclinations calculated using our smoothing method on a 3D high energy X-ray diffraction microscopy (HEDM) dataset to those determined by meshing the GBs. The two approaches determined similar GB plane distributions, though they varied significantly at triple junctions. Finally, the smoothing method was demonstrated for two sources of 3D voxelated grain structures: HEDM data and results from Monte Carlo Potts grain growth simulations.

关键词： Grain boundary structure 3D Reconstruction smoothing algorithm

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A G² Continuous Path-smoothing algorithm Using Modified Quadratic Polynomial Interpolation

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2014年第2期11卷 25-25页

作者： Huh, Uk-Youl Chang, Seong-Ryong Inha Univ Inchon South Korea

Path searching algorithm is one of the main topics in studies on path planning. These algorithms are used to avoiding obstacles and find paths from starting point to target point. There are dynamic problems that must be addressed when these paths are applied in real environments. In order to be applicable in actual situations, the path must be a smooth path. A smooth path is a path that maintains continuity. Continuity is decided by the differential values of the path. In order to be G(2) continuous, the secondary differential values of the path must be connected throughout the path. In this paper, the interpolation method is used to construct continuous paths. The quadratic polynomial interpolation is a simple method for obtaining continuous paths about three points. The proposed algorithm makes a connection of three points with curves and the proposed path is rotated using the parametric method in order to make the path optimal and smooth. The polynomials expand to the next three points and they merge into the entire path using the membership functions with G(2) continuity.

关键词： Continuous Path Curve Fitting Function Approximation Interpolation Path Planning Robot Motion smoothing algorithm Smooth Path Vehicle Navigation

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New smoothing SVM algorithm with tight error bound and efficient reduced techniques

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第3期56卷 599-617页

作者： Zhou, Shuisheng Cui, Jiangtao Ye, Feng Liu, Hongwei Zhu, Qiang Xidian Univ Sch Sci Xian 710071 Peoples R China Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China

The quadratically convergent algorithms for training SVM with smoothing methods are discussed in this paper. By smoothing the objective function of an SVM formulation, Lee and Mangasarian [Comput. Optim. Appl. 20(1):5-22, 2001] presented one such algorithm called SSVM and proved that the error bound between the new smooth problem and the original one was for large positive smoothing parameter p. We derive a new method by smoothing the optimality conditions of the SVM formulation, and we prove that the error bound is , which is better than Lee and Mangasarian's result. Based on SMW identity and updating Hessian iteratively, some boosting skills are proposed to solve Newton equation with lower computational complexity for reduced smooth SVM algorithms. Many experimental results show that the proposed smoothing method has the same accuracy as SSVM, whose error bound is also tightened to in this paper, and the proposed boosting skills are efficient for solving large-scale problems by RSVM.

关键词： SSVM smoothing algorithm Error bound Reduced methods

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