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Certifying the global optimality of Quartic Minimization over the Sphere

Journal of the Operations Research Society of China 2022年第2期10卷 241-287页

作者： Sheng-Long Hu Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018ZhejiangChina

The quartic minimization over the sphere is an NP-hard problem in the general *** exist various methods for computing an approximate solution for any given *** practice,it is quite often that a global optimal solution was found but without a *** will present in this article two classes of methods which are able to certify the global optimality,i.e.,algebraic methods and semidefinite program(SDP)relaxation *** advances on these topics are summarized,accompanied with some emerged new *** want to emphasize that for mediumor large-scaled instances,the problem is still a challenging one,due to an apparent limitation on the current force for solving SDP problems and the intrinsic one on the approximation techniques for the problem.

关键词： Quartic minimization Tensor Sphere global optimality Elimination method Critical points Eigenvectors Determinant Nondegenerate Characteristic polynomial SDP relaxations Moment matrix Flatness Positivstellensatz Nonnegative polynomial Sums of squares Duality

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Self-tuning White Noise Deconvolution Fuser with Asymptotic global optimality

Self-tuning White Noise Deconvolution Fuser with Asymptotic ...

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2010 Chinese Control and Decision Conference

作者： Xiaojun Sun,Zili Deng Department of Automation,Heilongjiang University,Harbin,150080,China

＜正＞White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration,communication,signal processing,and state *** the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics,an on-line noise statistics estimator is given by the correlation *** the Kalman filtering method,based on the self-tuning Riccati equation,a self-tuning weighted measurement fusion white noise deconvolution estimator is *** the dynamic error system analysis（DESA） method,it is proved that the self-tuning white noise deconvolution fuser converges to the steady-state optimal white noise deconvolution fuser in a realization so that it has the asymptotic global optimality.A simulation example for a 3-sensor system with Bernoulli-Gaussian input white noise shows its effectiveness.

关键词： Multisensor Information Fusion Weighted Measurement Fusion Self-tuning Fuser White Noise Deconvolution global optimality Kalman Filtering Convergence

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Multi-sensor optimal weighted fusion incremental Kalman smoother

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Journal of Systems Engineering and Electronics 2018年第2期29卷 262-268页

作者： SUN Xiaojun YAN Guangming Electrical Engineering Institute Heilongjiang University

In practical applications, the system observation error is widespread. If the observation equation of the system has not been verified or corrected under certain environmental conditions,the unknown system errors and filtering errors will come into *** incremental observation equation is derived, which can eliminate the unknown observation errors effectively. Furthermore, an incremental Kalman smoother is presented. Moreover, a weighted measurement fusion incremental Kalman smoother applying the globally optimal weighted measurement fusion algorithm is *** simulation results show their effectiveness and feasibility.

关键词： weighted fusion incremental Kalman filtering poor observation condition Kalman smoother global optimality

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Time-varying optimal distributed fusion white noise deconvolution estimator

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Frontiers of Electrical and Electronic Engineering in China 2012年第3期7卷 318-325页

作者： Xiaojun SUN Guangming YAN College of Electrical Engineering Heilongjiang University Harbin150080 China

White noise deconvolution has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. Using the Kalman filtering method, the time-varying optimal dis- tributed fusion white noise deconvolution estimator is presented for the multisensor linear discrete time-varying systems. It is derived from the centralized fusion white noise deconvolution estimator so that it is identical to the centralized fuser, i.e., it has the global optimality. It is superior to the existing distributed fusion white noise estimators in the optimality and the complexity of computation. A Monte Carlo simulation for the Bemoulli- Gaussian input white noise shows the effectiveness of the proposed results.

关键词： multisensor information fusion distributedfusion white noise deconvolution global optimality Kal-man filtering

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SELF-TUNING WEIGHTED MEASUREMENT FUSION WHITE NOISE DECONVOLUTION ESTIMATOR

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Journal of Electronics(China) 2010年第1期27卷 51-59页

作者： Sun Xiaojun Deng Zili Department of Automation Heilongjiang University Harbin 150080 China

For the multi-sensor linear discrete time-invariant stochastic systems with correlated measurement noises and unknown noise statistics,an on-line noise statistics estimator is obtained using the correlation *** it into the optimal weighted fusion steady-state white noise deconvolution estimator based on the Kalman filtering,a self-tuning weighted measurement fusion white noise deconvolution estimator is *** the Dynamic Error System Analysis(DESA) method,it proved that the self-tuning fusion white noise deconvolution estimator converges to the steady-state optimal fusion white noise deconvolution estimator in a ***,it has the asymptotically global optimality.A simulation example for the tracking system with 3 sensors and the Bernoulli-Gaussian input white noise shows its effectiveness.

关键词： Multi-sensor information fusion Self-tuning fuser White noise deconvolution global optimality Convergence

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Dynamic Tabu Search Algorithm for Solving Departure Scheduling Problem

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Journal of Southwest Jiaotong University(English Edition) 2007年第2期15卷 132-137页

作者：王来军史忠科雷秀娟 School of Automatization Northwestern Polytechnical University

The aircraft departure scheduling problem is described comprehensively. A mathematical model is built for solving this problem. Then, a local search algorithm is proposed; based on it, the dynamic tabu search technique is applied, and the related implement techniques are presented. A simulation including condition and results is performed to solve a representative problem. It is concluded that （ 1 ） departure aircrafts of each queue keep the same order comparatively all the lime, and the distribution of the departure time is well-proportioned, which accords with the ＂first-come first-serve＂ principle; （2） the total time costs are minimized, which would economize money and reduce danger; （ 3 ） the optimization result is not exclusive, which means that several approaches can be chosen at will; （4） the solution obtained is the global optimal one, which guarantees the validity of the proposed method.

关键词： Departure scheduling Wake vortex separation global optimality Tabu search

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Steady-state Optimal Measurement Fusion White Noise Deconvolution Estimators

Steady-state Optimal Measurement Fusion White Noise Deconvol...

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2009中国控制与决策会议

作者： Xiao-Jun Sun,Zi-Li Deng Department of Automation,Heilongjiang University,Harbin 150080,China

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration,communication,signal processing,and state *** the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises,a steady-state measurement fusion system is obtained by the weighted least square(WLS) method.A steady-state optimal weighted measurement fusion white noise deconvolution estimator is presented using the Kalman filtering *** a new derivation method,it is rigorously proved that the steady-state white noise deconvolution fuser is numerically identical to the centralized steady-state white noise deconvolution fuser,*** has the asymptotically global *** can reduce the computational burden because of the lower dimension of the measurement vector.A simulation example for the Bernoulli-Gaussian input white noise shows the effectiveness of the proposed results.

关键词： Multisensor Information Fusion Weighted Measurement Fusion White Noise Deconvolution global optimality Kalman Filtering

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