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数学与物理
应用数学进展
Vol. 5 No. 4 (November 2016)
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SQP子问题解集的有限收敛性
Finite Convergence of the Solution Set for SQP Subproblem
DOI:
10.12677/AAM.2016.54072
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被引量
下载: 1,916
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国家自然科学基金支持
作者:
顾亚静
,
赵文玲
:山东理工大学理学院,山东 淄博
关键词:
序列二次规划方法的子问题
;
多参数规划
;
可行解序列
;
弱强集
;
有限收敛
;
Subproblems of Sequential Quadratic Programming
;
Multi-Paramatic Programming
;
Feasible Solution Sequence
;
Weak Sharp Set
;
Finite Convergence
摘要:
序列二次规划方法(SQP)是求解约束优化问题的最有效的方法之一。SQP方法求解过程中产生的子问题是一个带参数的二次规划问题(SQP多参数规划子问题)。本文在SQP多参数规划子问题中,引入了其解集弱强的概念,讨论了弱强集的性质,并在其解集是弱强的条件下,给出了由任意算法所产生的可行解序列有限收敛的必要与充分条件。
Abstract:
Sequential Quadratic Programming (SQP) method is one of the most effective methods for solving constrained optimization problems. There is a class of subproblems during the process via SQP method. The subproblem which is called SQP multi-parameter subproblem is a multi-parametric quadratic programming. In this work, we introduce weak sharp solution set into SQP multi-pa- rameter subproblem. The character of weak sharp solution set is discussed. Under weak sharp conditions of solution set, the sufficient and necessary condition for finite convergence of feasible solution sequence via any algorithm is obtained.
文章引用:
顾亚静, 赵文玲. SQP子问题解集的有限收敛性[J]. 应用数学进展, 2016, 5(4): 620-629.
http://dx.doi.org/10.12677/AAM.2016.54072
参考文献
[
1
]
Fiacco, A.V. (1983) Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York.
[
2
]
Grancharova, A. and Johansen, T.A. (2012) Multi-Parametric Programming. Lecture Notes in Control and Information Sciences, 429, 1-37.
http://dx.doi.org/10.1007/978-3-642-28780-0_1
[
3
]
Diehl, M., Uslu, I., et al. (2001) Real-Time Optimi-zation for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column. Online Optimization of Large Scale Systems. Springer Berlin, Heidelberg, 363-383.
[
4
]
https://www.researchgate.net/publication/27279305_Real-Time_Optimization_for_Large_Scale_Processes_Nonlinear_Model_Predictive_Control_of_a_High_Purity_Distillation_Column
[
5
]
Mostafa, E.S. (2012) An SQP Trust Region Method for Solving the Discrete-Time Linear Quadratic Control Problem. International Journal of Applied Mathematics and Computer Science, 22, 353-363.
http://dx.doi.org/10.2478/v10006-012-0026-5
[
6
]
Mostafa, E.S., Ismail, H.G. and Al-Afandi, N.F. (2013) An SQP Augmented Lagrangian Method for Two Classes of Nonlinear Semidefinite Programming Problems Arising in Discrete-Time Feedback Control. Pacific Journal of Optimization, 9, 511-534.
[
7
]
Kungurtsev, V. (2013) Second-Derivative Sequential Quadratic Programming Methods for Nonlinear Optimization. Dissertations and Theses, Gradworks.
[
8
]
Kungurtsev, V. and Diehl, M. (2014) SQP Methods for Parametric Nonlinear Optimization.
http://www.optimization-online.org/DB_FILE/2014/02/4255.pdf
[
9
]
Burke, J.V. and Ferris, M.C. (1993) Weak Sharp Minima in Mathematical Programming. SIAM Journal on Control and Optimization, 31, 1340-1359.
http://dx.doi.org/10.1137/0331063
[
10
]
Ferris, M.C. (1991) Finite Termination of the Proximal Point Algorithm. Mathematical Programming, 50, 359-366.
http://dx.doi.org/10.1007/BF01594944
[
11
]
Matsushita, S.Y. and Xu, L. (2012) Finite Termination of the Proximal Point Al-gorithm in Banach Spaces. Journal of Mathematical Analysis and Applications, 387, 765-769.
http://dx.doi.org/10.1016/j.jmaa.2011.09.032
[
12
]
Rockafellar, R.T. (1976) Monotone Operators and the Proximal Point Algo-rithm. SIAM Journal on Control and Optimization, 14, 877-898.
http://dx.doi.org/10.1137/0314056
[
13
]
Zhou, J.C. and Wang, C.Y. (2012) New Characterizations of Weak Sharp Minima. Optimization Letters, 6, 1773-1785.
http://dx.doi.org/10.1007/s11590-011-0369-0
[
14
]
Gupta, A., Bhartiya, S. and Nataraj, P.S.V. (2011) A Novel Approach to Multi-Parametric Quadratic Programming. Automatica, 47, 2112-2117.
https://www.researchgate.net/publication/220158033_A_novel_approach_to_multiparametric_quadratic_programming
[
15
]
Burke, J.V. and More, J.J. (1988) On the Identification of Active Constraints. SIAM Journal on Numerical Analysis, 25, 1197-1211.
http://dx.doi.org/10.1137/0725068
[
16
]
Wang, C.Y., Liu, Q. and Yang, X.M. (2005) Convergence Properties of Nonmonotone Spectral Projected Gradient Methods. Journal of Computational and Applied Mathematics, 182, 51-66.
http://dx.doi.org/10.1016/j.cam.2004.10.018
[
17
]
Wang, C.Y., Zhao, W.L., Zhou, J.H. and Lian, S.J. (2013) Global Convergence and Finite Termination of a Class of Smooth Penalty Function Algorithms. Optimization Methods and Software, 28, 1-25.
http://dx.doi.org/10.1080/10556788.2011.579965
[
18
]
Xiu, N.H. and Zhang, J.Z. (2003) Some Recent Advances in Projec-tion-Type Methods for Variational Inequalities. Journal of Computational and Applied Mathematics, 152, 559-585.
http://dx.doi.org/10.1016/S0377-0427(02)00730-6
[
19
]
Marcotte, P. and Zhu, D.L. (1998) Weak Sharp Solutions of Variational Inequalities. SIAM Journal on Optimization, 9, 179-189.
http://dx.doi.org/10.1137/S1052623496309867
[
20
]
Xiu, N.H. and Zhang, J.Z. (2005) On Finite Convergence of Proximal Point Algorithms for Variational Inequalities. Journal of Mathematical Analysis and Applications, 312, 148-158.
http://dx.doi.org/10.1016/j.jmaa.2005.03.026
[
21
]
Rockafellar, R.T. and Wets, R.J. (1998) Variational Analysis. Springer, New York.
http://dx.doi.org/10.1007/978-3-642-02431-3
[
22
]
Zhao, W.L. and Song, D.J. (2007) A Global Error Bound via the SQP Me-thod for Constrained Optimization Problem. Journal of Industrial and Management Optimization, 3, 775-781.
http://www.aimsciences.org/journals/displayArticles.jsp?paperID=2746
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