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15 April 2019, Volume 36 Issue 2 Previous Issue    Next Issue

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A Descent Alternating Direction Method of Multipliers with Random Step Size for Structured Optimization Problem ZHANG Yan-na, SHEN Yuan, SUN Li-ming 2019, 36 (2):  123-137.  doi: 10.3969/j.issn.1005-3085.2019.02.001 Abstract ( 241 )   PDF (199KB) ( 356 )   Save In this paper, we consider the structured convex optimization problem with two blocks of variables. The alternating direction method of multipliers (ADMM) is a classical method for solving this problem, which is based on the augmented Lagrange algorithm and it utilizes the separability of two blocks of variables in the objective function to simplify the computation of subproblems. The descent alternating direction method of multipliers (DADMM) is an improved version of ADMM, which applies an optimal step as well as a fixed factor to do extension on  part of the variables. The DADMM is reported to be faster than the classical ADMM in numerical simulations. According to the idea of SC-Method proposed by Xu which allows the extension factor to be randomly generated, we propose a new DADMM with random step size. The convergence of the new algorithm can be derived under mild assumptions. Preliminary experiments demonstrate the promising performance and dimensional scalability of the new method. Related Articles | Metrics

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Improved Algorithm for Non-equidistant NGM$(1,1,k)$ Model and Its Applications ZHANG Kai, WANG Cheng-yong, HE Li-juan 2019, 36 (2):  138-154.  doi: 10.3969/j.issn.1005-3085.2019.02.002 Abstract ( 252 )   PDF (235KB) ( 333 )   Save According to the non-equidistance of observation data and the deficiency of NGM$(1,1,k)$ model, a modeling approach for the grey action quantity with non-equidistant NGM$(1,1,k)$ model is established in this paper. A new model's background value optimization method is proposed based on the principle of numerical integration by using non-equidistance Simpson numerical integration formula. Then the desirability function is construsted by the minimizing the square sum of relative error between the raw sequence and the simulative sequence, which is used to determine the optimal constant value in the time response function. Moreover, a complete improved algorithm for non-equidistance NGM$(1,1,k)$ model is proposed. Finally, the efficiency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to significantly improve the simulation and prediction accuracy. Related Articles | Metrics

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Variation Analysis for Common Machining Processes Based on a Multivariate Semi-parametric Regression Model ZHANG Lei, DONG Yan, WANG Lei, ZHAO En-lan, HUANG Chuan-hui 2019, 36 (2):  155-164.  doi: 10.3969/j.issn.1005-3085.2019.02.003 Abstract ( 227 )   PDF (477KB) ( 321 )   Save Variation analysis for common machining processes aims to reduce variation sources and improve manufacturing quality. Researchers have attempted many methods to recognize the rules of variation sources acting on the machining elements. However, the methods have their own limitations individually due to the complexity of the machining errors. In this paper, a multivariate semi-parametric regression model based on the mathematical analysis and the engineering experiences is proposed to face the variation analysis challenge in common machining processes. The parametric estimation and non-parametric rule identification are discussed in detail based on the measured data. A simulation case indicates that compared with the existing method, the proposed model not only is able to accurately estimate the variation streamed from previous machining stations, but also effectively identify the system errors at current station. The research provides a foundation for variation analysis in common machining processes. Related Articles | Metrics

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The Asymptotic Stability of the Kink Profile Solitary-wave Solution for the Fluidized-bed Modeling Equation ZHANG Dong-jie, ZHANG Wei-guo, YONG Yan, LI Xiang 2019, 36 (2):  165-178.  doi: 10.3969/j.issn.1005-3085.2019.02.004 Abstract ( 241 )   PDF (171KB) ( 284 )   Save The fluidized-bed modeling equation is an important model in the dynamics of two-phase flow. In this paper, we consider the asymptotic stability of the monotone decreasing kink profile solitary-wave solution of the equation. At first, we obtain the first and second derivative estimates of the kink profile solitary-wave solution. Then according to the technical energy estimation and Young inequalities, we overcome the difficulty caused by the complex dissipative term, and establish the uniformly energy estimate for the perturbation of the traveling wave solution. Finally, we prove that the monotone decreasing kink profile solitary-wave solution is asymptotically stable. Related Articles | Metrics

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A Class of Nonlinear Generalized Strong Damping Time Delay Disturbed Sine-Gordon Equation Initial Value Problem FENG Yi-hu, WANG Wei-gang, MO Jia-qi 2019, 36 (2):  179-186.  doi: 10.3969/j.issn.1005-3085.2019.02.005 Abstract ( 152 )   PDF (141KB) ( 486 )   Save In this paper, a class of nonlinear generalized Sine-Gordon disturbed equation is considered. From the asymptotic theory, the asymptotic analytic solution to corresponding equation time delay initial value problem is solved. Firstly, the outer solution is found by using the Fourier transform method. Secondly, the disturbed function is developed from the time delay variable. Then, the uniformly valid solution to the strong damping time delay disturbed generalized Sine-Gordon equation initial value problem is obtained by the perturbation method and theory. Moreover, the asymptotic solution is an analytic expansion, and able to do analytic operation. Therefore, the corresponding physical characters are derived, and application fields are enlarged. Related Articles | Metrics

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Two Modified Augmented Lagrange Multiplier Algorithms with Median Value Toeplitz Matrix Compressive Recovery NIU Jian-hua, WANG Chuan-long 2019, 36 (2):  187-197.  doi: 10.3969/j.issn.1005-3085.2019.02.006 Abstract ( 212 )   PDF (176KB) ( 391 )   Save The augmented Lagrange multiplier algorithm is an effective iteration method for solving matrix compressive recovery. To solve the Toeplitz matrix compressive recovery model effectively, two modified augmented Lagrange multiplier algorithms with median value are proposed in this paper. In the new algorithms, the iterated matrix generated by the augmented Lagrange multiplier algorithm is modified by median value and its Toeplitz structure is guaranteed. The new algorithms not only reduce the SVD time and CPU time, but also obtain a more accurate iterative matrix. Meanwhile, the convergence analysis of the two new algorithms are also given in detail. Finally, the numerical examples are presented to confirm their feasibility and effectiveness. The numerical implementations also show that the new algorithms have advantage over the augmented Lagrange multiplier algorithm in computation time and accuracy. Related Articles | Metrics

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Stability of Multistage Stochastic Programs with Quadratic Objective Functions JIANG Jie, CHEN Zhi-ping 2019, 36 (2):  198-218.  doi: 10.3969/j.issn.1005-3085.2019.02.007 Abstract ( 221 )   PDF (156KB) ( 392 )   Save Multistage stochastic programs can properly describe complex long-term decision-making problems under uncertainty. We study the quantitative stability of multistage stochastic programs with quadratic objective functions under perturbations of the underlying stochastic processes, which extend the current results for the linear objective functions. We first derive the upper bounds of feasible solutions through parametric programming theories. In order to obtain the Lipschitz continuities of recourse functions, we assume the continuity of the conditional distributions under the Fortet-Mourier metric. With these preparations, we finally establish the Lipschitz continuity of the optimal value function. Our quantitative stability results do not rely on the filtration distance. Related Articles | Metrics

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Dynamical Behaviors of a Three Species Predator-prey System with Predator Stage-structure and Impulsive Effects LIU Qin, SHAO Yuan-fu, ZHOU Si, CHEN Hai-ru 2019, 36 (2):  219-242.  doi: 10.3969/j.issn.1005-3085.2019.02.008 Abstract ( 156 )   PDF (33662KB) ( 46 )   Save Considering the impulsive effects at different fixed moments and the predator stage-structure, we propose a three species predator-prey system with predator stage-structure and impulsive effects in this paper. At first, we prove the existence, stability and global attractivity of the prey-extinction periodic solution via the Floquent theory and small amplitude perturbation. Then, we obtain the permanence of this system by using comparison method and involving multiple Laypunov functions. Finally, we show our theoretical results by numerical simulations, such as time series of species population and chaotic bands of system. Related Articles | Metrics