-
Previous Article
On general form of the Tanh method and its application to nonlinear partial differential equations
- NACO Home
- This Issue
-
Next Article
Solving Malfatti's high dimensional problem by global optimization
A new smoothing approach to exact penalty functions for inequality constrained optimization problems
1. | Suleyman Demirel University, Department of Mathematics, Isparta, 32100, Turkey, Turkey, Turkey |
References:
[1] |
A. M. Bagirov, A. Al Nuamiat and N. Sultanova, Hyperbolic smoothing functions for nonsmooth minimization, Optimization, 62 (2013), 759-782.
doi: 10.1080/02331934.2012.675335. |
[2] |
F. S. Bai, Z. Y. Wu and D. L. Zhu, Lower order calmness and exact penalty fucntion, Optimization Methods ans Software, 21 (2006), 515-525.
doi: 10.1080/10556780600627693. |
[3] |
A. Ben-Tal and M. Teboule, Smoothing technique for nondifferentiable optimization problems, Lecture notes in mathematics, 1405, Springer-Verlag, Heidelberg, (1989), 1-11. |
[4] |
D. Bertsekas, Nondifferentiable optimization via approximation, Mathematical Programming Study, 3 (1975), 1-25. |
[5] |
C. Chen and O. L. Mangasarian, A Class of smoothing functions for nonlinear and mixed complementarity problem, Computational Optimization and Application, 5 (1996), 97-138.
doi: 10.1007/BF00249052. |
[6] |
X. Chen, Smoothing Methods for nonsmooth, nonconvex minimzation, Mathematical Programming Serie B, 134 (2012), 71-99.
doi: 10.1007/s10107-012-0569-0. |
[7] |
S. J. Lian, Smoothing approximation to l1 exact penalty for inequality constrained optimization, Applied Mathematics and Computation, 219 (2012), 3113-3121.
doi: 10.1016/j.amc.2012.09.042. |
[8] |
B. Liu, On smoothing exact penalty function for nonlinear constrained optimization problem, Journal of Applied Mathematics and Computing, 30 (2009), 259-270.
doi: 10.1007/s12190-008-0171-z. |
[9] |
M. C. Pinar and S. Zenios, On smoothing exact penalty functions for convex constrained optimization, SIAM Journal on Optimization, 4 (1994), 468-511.
doi: 10.1137/0804027. |
[10] |
Z. Meng, C. Dang, M. Jiang and R. Shen, A smoothing objective penalty function algorithm foe inequality constrained optimization problems, Numerical Functional Analysis and Optimization, 32 (2011), 806-820.
doi: 10.1080/01630563.2011.577262. |
[11] |
Z. Y. Wu, H. W. J. Lee, F. S. Bai and L. S. Zhang, Quadratic smoothing approximation to l1 exact penalty function in global optimization, Journal of Industrail and Management Optimization, 53 (2005), 533-547.
doi: 10.3934/jimo.2005.1.533. |
[12] |
Z. Y. Wu, F. S. Bai, X. Q. Yang and L. S. Zhang, An exact lower orderpenalty function and its smoothing in nonlinear programming, Optimization, 53 (2004), 51-68.
doi: 10.1080/02331930410001662199. |
[13] |
A. E. Xavier, The hyperbolic smoothing clustering method, Pattern Recognition, 43 (2010), 731-737. |
[14] |
A. E. Xavier,A. A. F. D. Oliveira, Optimal covering of plane domains by circles via hyperbolic smoothing, Journal of Global Optimization, 31 (2005), 493-504.
doi: 10.1007/s10898-004-0737-8. |
[15] |
X. Xu, Z. Meng, J. Sun and R. Shen, A penalty function method based on smoothing lower order penalty function, Journal of Computational and Applied Mathematics, 235 (2011), 4047-4058.
doi: 10.1016/j.cam.2011.02.031. |
[16] |
N. Yilmaz, A. Sahiner, A New Global Optimization Technique Based on the Smoothing Approach for Non-smooth, Non-convex Optimization,, Submitted., ().
|
[17] |
N. Yilmaz, A. Sahiner, Smoothing Approach for Non-lipschitz Optimization,, Submitted., ().
|
[18] |
I. Zang, A smooting out technique for min-max optimization, Mathematical Programming, 19 (1980), 61-77.
doi: 10.1007/BF01581628. |
[19] |
W. I. Zangwill, Nonlinear programing via penalty functions, Management Science, 13 (1967), 344-358. |
show all references
References:
[1] |
A. M. Bagirov, A. Al Nuamiat and N. Sultanova, Hyperbolic smoothing functions for nonsmooth minimization, Optimization, 62 (2013), 759-782.
doi: 10.1080/02331934.2012.675335. |
[2] |
F. S. Bai, Z. Y. Wu and D. L. Zhu, Lower order calmness and exact penalty fucntion, Optimization Methods ans Software, 21 (2006), 515-525.
doi: 10.1080/10556780600627693. |
[3] |
A. Ben-Tal and M. Teboule, Smoothing technique for nondifferentiable optimization problems, Lecture notes in mathematics, 1405, Springer-Verlag, Heidelberg, (1989), 1-11. |
[4] |
D. Bertsekas, Nondifferentiable optimization via approximation, Mathematical Programming Study, 3 (1975), 1-25. |
[5] |
C. Chen and O. L. Mangasarian, A Class of smoothing functions for nonlinear and mixed complementarity problem, Computational Optimization and Application, 5 (1996), 97-138.
doi: 10.1007/BF00249052. |
[6] |
X. Chen, Smoothing Methods for nonsmooth, nonconvex minimzation, Mathematical Programming Serie B, 134 (2012), 71-99.
doi: 10.1007/s10107-012-0569-0. |
[7] |
S. J. Lian, Smoothing approximation to l1 exact penalty for inequality constrained optimization, Applied Mathematics and Computation, 219 (2012), 3113-3121.
doi: 10.1016/j.amc.2012.09.042. |
[8] |
B. Liu, On smoothing exact penalty function for nonlinear constrained optimization problem, Journal of Applied Mathematics and Computing, 30 (2009), 259-270.
doi: 10.1007/s12190-008-0171-z. |
[9] |
M. C. Pinar and S. Zenios, On smoothing exact penalty functions for convex constrained optimization, SIAM Journal on Optimization, 4 (1994), 468-511.
doi: 10.1137/0804027. |
[10] |
Z. Meng, C. Dang, M. Jiang and R. Shen, A smoothing objective penalty function algorithm foe inequality constrained optimization problems, Numerical Functional Analysis and Optimization, 32 (2011), 806-820.
doi: 10.1080/01630563.2011.577262. |
[11] |
Z. Y. Wu, H. W. J. Lee, F. S. Bai and L. S. Zhang, Quadratic smoothing approximation to l1 exact penalty function in global optimization, Journal of Industrail and Management Optimization, 53 (2005), 533-547.
doi: 10.3934/jimo.2005.1.533. |
[12] |
Z. Y. Wu, F. S. Bai, X. Q. Yang and L. S. Zhang, An exact lower orderpenalty function and its smoothing in nonlinear programming, Optimization, 53 (2004), 51-68.
doi: 10.1080/02331930410001662199. |
[13] |
A. E. Xavier, The hyperbolic smoothing clustering method, Pattern Recognition, 43 (2010), 731-737. |
[14] |
A. E. Xavier,A. A. F. D. Oliveira, Optimal covering of plane domains by circles via hyperbolic smoothing, Journal of Global Optimization, 31 (2005), 493-504.
doi: 10.1007/s10898-004-0737-8. |
[15] |
X. Xu, Z. Meng, J. Sun and R. Shen, A penalty function method based on smoothing lower order penalty function, Journal of Computational and Applied Mathematics, 235 (2011), 4047-4058.
doi: 10.1016/j.cam.2011.02.031. |
[16] |
N. Yilmaz, A. Sahiner, A New Global Optimization Technique Based on the Smoothing Approach for Non-smooth, Non-convex Optimization,, Submitted., ().
|
[17] |
N. Yilmaz, A. Sahiner, Smoothing Approach for Non-lipschitz Optimization,, Submitted., ().
|
[18] |
I. Zang, A smooting out technique for min-max optimization, Mathematical Programming, 19 (1980), 61-77.
doi: 10.1007/BF01581628. |
[19] |
W. I. Zangwill, Nonlinear programing via penalty functions, Management Science, 13 (1967), 344-358. |
[1] |
Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial and Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895 |
[2] |
Z.Y. Wu, H.W.J. Lee, F.S. Bai, L.S. Zhang. Quadratic smoothing approximation to $l_1$ exact penalty function in global optimization. Journal of Industrial and Management Optimization, 2005, 1 (4) : 533-547. doi: 10.3934/jimo.2005.1.533 |
[3] |
Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial and Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485 |
[4] |
Zhongwen Chen, Songqiang Qiu, Yujie Jiao. A penalty-free method for equality constrained optimization. Journal of Industrial and Management Optimization, 2013, 9 (2) : 391-409. doi: 10.3934/jimo.2013.9.391 |
[5] |
Yibing Lv, Zhongping Wan. Linear bilevel multiobjective optimization problem: Penalty approach. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1213-1223. doi: 10.3934/jimo.2018092 |
[6] |
Na Zhao, Zheng-Hai Huang. A nonmonotone smoothing Newton algorithm for solving box constrained variational inequalities with a $P_0$ function. Journal of Industrial and Management Optimization, 2011, 7 (2) : 467-482. doi: 10.3934/jimo.2011.7.467 |
[7] |
Boshi Tian, Xiaoqi Yang, Kaiwen Meng. An interior-point $l_{\frac{1}{2}}$-penalty method for inequality constrained nonlinear optimization. Journal of Industrial and Management Optimization, 2016, 12 (3) : 949-973. doi: 10.3934/jimo.2016.12.949 |
[8] |
Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial and Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381 |
[9] |
Ming Chen, Chongchao Huang. A power penalty method for a class of linearly constrained variational inequality. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1381-1396. doi: 10.3934/jimo.2018012 |
[10] |
Ahmet Sahiner, Nurullah Yilmaz, Gulden Kapusuz. A novel modeling and smoothing technique in global optimization. Journal of Industrial and Management Optimization, 2019, 15 (1) : 113-130. doi: 10.3934/jimo.2018035 |
[11] |
Elmehdi Amhraoui, Tawfik Masrour. Smoothing approximations for piecewise smooth functions: A probabilistic approach. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021033 |
[12] |
Zhiqing Meng, Qiying Hu, Chuangyin Dang. A penalty function algorithm with objective parameters for nonlinear mathematical programming. Journal of Industrial and Management Optimization, 2009, 5 (3) : 585-601. doi: 10.3934/jimo.2009.5.585 |
[13] |
Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial and Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705 |
[14] |
Xiaodi Bai, Xiaojin Zheng, Xiaoling Sun. A survey on probabilistically constrained optimization problems. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 767-778. doi: 10.3934/naco.2012.2.767 |
[15] |
Yafeng Li, Guo Sun, Yiju Wang. A smoothing Broyden-like method for polyhedral cone constrained eigenvalue problem. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 529-537. doi: 10.3934/naco.2011.1.529 |
[16] |
Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial and Management Optimization, 2008, 4 (2) : 353-362. doi: 10.3934/jimo.2008.4.353 |
[17] |
Lianjun Zhang, Lingchen Kong, Yan Li, Shenglong Zhou. A smoothing iterative method for quantile regression with nonconvex $ \ell_p $ penalty. Journal of Industrial and Management Optimization, 2017, 13 (1) : 93-112. doi: 10.3934/jimo.2016006 |
[18] |
Kai Zhang, Song Wang. Convergence property of an interior penalty approach to pricing American option. Journal of Industrial and Management Optimization, 2011, 7 (2) : 435-447. doi: 10.3934/jimo.2011.7.435 |
[19] |
Kai Zhang, Xiaoqi Yang, Kok Lay Teo. A power penalty approach to american option pricing with jump diffusion processes. Journal of Industrial and Management Optimization, 2008, 4 (4) : 783-799. doi: 10.3934/jimo.2008.4.783 |
[20] |
Shiyun Wang, Yong-Jin Liu, Yong Jiang. A majorized penalty approach to inverse linear second order cone programming problems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 965-976. doi: 10.3934/jimo.2014.10.965 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]