We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.
Bental, A. and Teboulle, M. (1989) A Smoothing Technique for Non-Differentiable Optimization Problems. Lecture Notes in Mathematics, Springer Verlag, Berlin, Vol. 1405, 1-11. https://doi.org/10.1007/BFb0083582
[3]
Pinar, M.C. and Zenios, S.A. (1994) On Smoothing Exact Penalty Functions for Convex Constarained Optimization. SIAM Journal on Optimization, 4, 486-511. https://doi.org/10.1137/0804027
[4]
Auslender, A., Cominetti, R. and Haddou, M. (1997) Asymptotic Analysis for Penalty and Barrier Methods in Convex and Linear Programming. Mathematics of Operational Research, 22, 43-62. https://doi.org/10.1287/moor.22.1.43
[5]
Gonzaga, C.C. and Castillo, R.A. (2003) A Nonlinear Programming Algorithm Based on Non-Coercive Penalty Functions. Mathematical Programming, 96, 87-101. https://doi.org/10.1007/s10107-002-0332-z
[6]
Wu, Z.Y., Bai, F.S., Yang, X.Q. and Zhang, L.S. (2004) An Exact Lower Order Penalty Function and Its Smoothing in Nonlinear Programming. Optimization, 53, 51-68. https://doi.org/10.1080/02331930410001662199
[7]
Meng, Z.Q., Dang, C.Y. and Yang, X.Q. (2006) On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization. Computational Optimization and Applications, 35, 375-398. https://doi.org/10.1007/s10589-006-8720-6
[8]
Herty, M., Klar, A., Singh, A.K. and Spellucci, P. (2007) Smoothed Penalty Algorithms for Optimization of Nonlinear Models. Computational Optimization and Applications, 37, 157-176. https://doi.org/10.1007/s10589-007-9011-6
[9]
Di Pillo, G., Lucidi, S. and Rinaldi, F. (2012) An Approach to Constrained Global Optimization Based on Exact Penalty Functions. Journal of Global Optimization, 54, 251-260. https://doi.org/10.1007/s10898-010-9582-0
[10]
Lian, S.J. (2012) Smoothing Approximation to l1 Exact Penalty Function for Inequality Constrained Optimization. Applied Mathematics and Computation, 219, 3113-3121. https://doi.org/10.1016/j.amc.2012.09.042
[11]
Xu, X.S., Meng, Z.Q., Sun, J.W., Huang, L.G. and Shen, R. (2013) A Second-Order Smooth Penalty Function Algorithm for Constarained Optimization Problems. Com-putational Optimization and Application, 55, 155-172. https://doi.org/10.1007/s10589-012-9504-9
[12]
Lian, S.J. and Duan, Y.Q. (2016) Smoothing of the Lower-Order Exact Penalty Function for Inequality Constrained Optimization. Journal of Inequalities and Applications, 185, 1-12. https://doi.org/10.1186/s13660-016-1126-9
[13]
Wu, Z.Y., Lee, H.W.J., Bai, F.S. and Zhang, L.S. (2017) Quadratic Smoothing Approximation to l1 Exact Penalty Function in Global Optimization. Journal of Industrial and Management Optimization, 1, 533-547. https://doi.org/10.3934/jimo.2005.1.533
[14]
Liu, B.Z. (2019) A Smoothing Penalty Function Method for the Constrained Optimization Problem. Open Journal of Optimization, 8, 113-126. https://doi.org/10.4236/ojop.2019.84010
