New Multiplier Algorithm for Nonlinear Programming with Inequality Constraints

被引:0
作者
Zhou, Jinchuan [1 ]
Xu, Xiuhua [2 ]
Tang, Jingyong [3 ]
机构
[1] Shandong Univ Technol, Sch Sci, Dept Math, Zibo 255049, Peoples R China
[2] Shandong Zibo Expt High Sch, Zibo 255090, Shandong, Peoples R China
[3] Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Peoples R China
来源
APPLIED MATHEMATICS & INFORMATION SCIENCES | 2012年 / 6卷 / 02期
基金
中国国家自然科学基金;
关键词
Augmented Lagrangian; Multiplier Algorithms; KKT points; AUGMENTED LAGRANGIAN-METHODS; GLOBAL OPTIMIZATION; CONVERGENCE;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce a new class of augmented Lagrangian function, which includes the well-known essential quadratic augmented Lagrangian as special cases. Based on this new function, we propose a multiplier algorithm, whose main feature is that the multiplier sequence does not require to be bounded. Global convergence to optimal solutions and KKT points are established, respectively.
引用
收藏
页码:337 / 343
页数:7
相关论文
共 19 条
[1]   ON AUGMENTED LAGRANGIAN METHODS WITH GENERAL LOWER-LEVEL CONSTRAINTS [J].
Andreani, R. ;
Birgin, E. G. ;
Martinez, J. M. ;
Schuverdt, M. L. .
SIAM JOURNAL ON OPTIMIZATION, 2008, 18 (04) :1286-1309
[2]  
Bertsekas D.P., 2019, Reinforcement learning and optimal control
[3]   Global minimization using an Augmented Lagrangian method with variable lower-level constraints [J].
Birgin, E. G. ;
Floudas, C. A. ;
Martinez, J. M. .
MATHEMATICAL PROGRAMMING, 2010, 125 (01) :139-162
[4]   Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization [J].
Birgin, Ernesto G. ;
Martinez, J. M. .
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2012, 51 (03) :941-965
[5]   Abstract convexity and augmented Lagrangians [J].
Burachik, Regina Sandra ;
Rubinov, Alex .
SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (02) :413-436
[6]   Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints [J].
Conn, AR ;
Gould, N ;
Sartenaer, A ;
Toint, PL .
SIAM JOURNAL ON OPTIMIZATION, 1996, 6 (03) :674-703
[7]  
Hestenes M. R., 1969, Journal of Optimization Theory and Applications, V4, P303, DOI 10.1007/BF00927673
[8]  
Khenkin E.I., 1976, USSR J COMPUTATIONAL, V16, P61
[9]   A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds [J].
Lewis, RM ;
Torczon, V .
SIAM JOURNAL ON OPTIMIZATION, 2002, 12 (04) :1075-1089
[10]   ON THE CONVERGENCE OF AUGMENTED LAGRANGIAN METHODS FOR CONSTRAINED GLOBAL OPTIMIZATION [J].
Luo, H. Z. ;
Sun, X. L. ;
Li, D. .
SIAM JOURNAL ON OPTIMIZATION, 2008, 18 (04) :1209-1230