PDF(135 KB)
Smoothing Approximation to the Square-Root Exact Penalty Function
Yaqiong DUAN, Shujun LIAN
Journal of Systems Science and Information ›› 2016, Vol. 4 ›› Issue (1) : 87-96.
PDF(135 KB)
PDF(135 KB)
Smoothing Approximation to the Square-Root Exact Penalty Function
In this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.
constrained optimization / exact penalty function / square-root penalty function / optimal solution / smoothing method {{custom_keyword}} /
[1] Zangwill W I. Non-linear programming via penalty functions. Management Science, 1967, 13: 344-358.
[2] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear programming: Theory and algorithms. 2nd ed. John Wiley Sons, Inc., New York, 1993.
[3] Bai F S, Luo X Y. Modified lower order penalty functions based on quadratic smoothing approximation. Operations Research Transactions, 2012, 16: 9-22.
[4] Lian S J. Smoothing approximation to l1 exact penalty function for inequality constrained optimization. Applied Mathematics and Computation, 2012, 219: 3113-3121.
[5] Sun X L, Li D. Value-estimation function method for for constrained global optimization. Journal of Optimization Theory and Applications, 1999, 24: 385-409.
[6] Wang C Y, Zhao W L, Zhou J C, et al. Global convergence and finite termination of a class of smooth penalty function algorithms. Optimization Methods and Software, 2013, 28: 1-25.
[7] Xu X S, Meng Z Q, Sun J W, et al. A second-order smooth penalty function algorithm for constrained optimization problems. Computational Optimization and Applications, 2013, 55: 155-172.
[8] Yang X Q, Meng Z Q, Huang X X, et al. Smoothing nonlinear penalty functions for constrained optimization. Numerical Functional Analysis and Optimization, 2003, 24: 351-364.
[9] Yu C J, Teo K L, Zhang L S, et al. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial and Management Optimization, 2010, 6: 895-910.
[10] Jiang M, Shen R, Xu X, et al. Second-order smoothing objective penalty function for constrained optimization problems. Numerical Functional Analysis and Optimization, 2014, 35: 294-309.
[11] Rubinov A M, Yang X Q, Bagirov A M. Penalty functions with a small penalty parameter. Optimization Methods and Software, 2002, 17: 931-964.
[12] Huang X X, Yang X Q. Convergence analysis of a class of nonlinear penalization methods for constrained optimization via first-order necessary optimality conditions. Journal of Optimization Theory and Applications, 2003, 116: 311-332.
[13] Wu Z Y, Bai F S, Yang X Q, et al. An exact lower order penalty function and its smoothing in nonlinear programming. Optimization, 2004, 53: 51-68.
[14] Meng Z Q, Dang C Y, Yang X Q. On the smoothing of the square-root exact penalty function for inequality constrained optimization. Computational Optimization and Applications, 2006, 35: 375-398.
[15] Lian S J. Smoothing approximation to the square-order exact penalty functions for constrained optimization. Journal of Applied Mathematics, 2013, Article ID 568316, 7 pages.
Supported by National Natural Science Foundation of China (71371107 and 61373027) and Natural Science Foundation of Shandong Provence (ZR2013AM013 and ZR2012AL07)
PDF(135 KB)
/
| 〈 |
|
〉 |
