[1] T. Antczak, A new exact exponential penalty function method and nonconvex mathematical pro-
gramming, Appl. Math. Comput. 217 (2011) 6652–6662.
[2] A.M. Bagirov, A. Al Nuaimat, N. Sultanova, Hyperbolic smoothing function method for minimax
problems, Optimization 62 (2013) 759–782.
[3] C. Chen, O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complemen-
tarity problem, Comput. Optim. Appl. 5 (1996) 97–138.
[4] X. Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math. Program. Ser. (B) 134
(2012) 71–99.
[5] F.S. Bai, Z.Y. Wu, D.L. Zhu, Lower order calmness and exact penalty function, Optim. Methods
Softw. 21 (2006) 515–525.
[6] D.P. Bertsekas, Nondifferentiable optimization via approximation, Math. Prog. Stud. 3 (1975) 1–25.
[7] G.D. Pillo, S. Lucidi, F. Rinaldi, An approach to constrained global optimization based on exact
penalty functions, J. Global Optim. 54 (2012) 251–260.
[8] M.V. Dolgopolik, Smooth exact penalty functions: a general approach, Optim. Lett. 10 (2016)
635–648.
[9] I. Eke, Combined heat and power economic dispatch by Taguchi-based filled function, Eng. Optim.
55 (2023) 791-805.
[10] I.I. Eremin,The penalty method in convex programming, Cybernet. Syst. Anal. 3 (1967) 53–56.
[11] A.V. Fiacco, G.P. McCormick, Nonlinear Programming, SIAM Philadelphia, 1990.
[12] C. Grossmann, M. Zadlo, A general class of penalty/ barrier path-following Newton methods for
nonlinear programming, Optimization 54 (2005) 161-190.
[13] M. Hassan, A. Baharum, Generalized logarithmic penalty function method for solving smooth non-
linear programming involving invex functions, Arab. J. Basic Appl. Sci. 26 (2019) 202–214.
[14] M. Hassan, S.A. Sulaiman, Logarithmic penalty function approach for enhancing the alkylation
process in Kaduna and Warri Refineries, Matematika 40 (2024) 17-25.
[15] J. Lee, D. Skipper, Virtuous smoothing for global optimization, J. Global Optim. 69 (2017) 677–
699.
[16] H. Liao, X. Yuan, R. Gao, An exact penalty function optimization method and its application in
stress constrained topology optimization and scenario based reliability design problems. Appl.
Math. Model. 125 (2024) 260-292.
[17] S.J. Lian, Smoothing approximation to l1 exact penalty for inequality constrained optimization,
Appl. Math. Comput. 219 (2012) 3113–3121.
[18] B. Liu, On smoothing exact penalty function for nonlinear constrained optimization problem, J.
Appl. Math. Comput. 30 (2009) 259–270.
[2] A.M. Bagirov, A. Al Nuaimat, N. Sultanova, Hyperbolic smoothing function method for minimax
problems, Optimization 62 (2013) 759–782.
[3] C. Chen, O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complemen-
tarity problem, Comput. Optim. Appl. 5 (1996) 97–138.
[4] X. Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math. Program. Ser. (B) 134
(2012) 71–99.
[5] F.S. Bai, Z.Y. Wu, D.L. Zhu, Lower order calmness and exact penalty function, Optim. Methods
Softw. 21 (2006) 515–525.
[6] D.P. Bertsekas, Nondifferentiable optimization via approximation, Math. Prog. Stud. 3 (1975) 1–25.
[7] G.D. Pillo, S. Lucidi, F. Rinaldi, An approach to constrained global optimization based on exact
penalty functions, J. Global Optim. 54 (2012) 251–260.
[8] M.V. Dolgopolik, Smooth exact penalty functions: a general approach, Optim. Lett. 10 (2016)
635–648.
[9] I. Eke, Combined heat and power economic dispatch by Taguchi-based filled function, Eng. Optim.
55 (2023) 791-805.
[10] I.I. Eremin,The penalty method in convex programming, Cybernet. Syst. Anal. 3 (1967) 53–56.
[11] A.V. Fiacco, G.P. McCormick, Nonlinear Programming, SIAM Philadelphia, 1990.
[12] C. Grossmann, M. Zadlo, A general class of penalty/ barrier path-following Newton methods for
nonlinear programming, Optimization 54 (2005) 161-190.
[13] M. Hassan, A. Baharum, Generalized logarithmic penalty function method for solving smooth non-
linear programming involving invex functions, Arab. J. Basic Appl. Sci. 26 (2019) 202–214.
[14] M. Hassan, S.A. Sulaiman, Logarithmic penalty function approach for enhancing the alkylation
process in Kaduna and Warri Refineries, Matematika 40 (2024) 17-25.
[15] J. Lee, D. Skipper, Virtuous smoothing for global optimization, J. Global Optim. 69 (2017) 677–
699.
[16] H. Liao, X. Yuan, R. Gao, An exact penalty function optimization method and its application in
stress constrained topology optimization and scenario based reliability design problems. Appl.
Math. Model. 125 (2024) 260-292.
[17] S.J. Lian, Smoothing approximation to l1 exact penalty for inequality constrained optimization,
Appl. Math. Comput. 219 (2012) 3113–3121.
[18] B. Liu, On smoothing exact penalty function for nonlinear constrained optimization problem, J.
Appl. Math. Comput. 30 (2009) 259–270.
[36] N. Yilmaz, H. Ogut, An exact penalty function approach for inequality constrained optimization
problems based on a new smoothing technique. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
72 (2023) 761-777.
[37] W. I. Zangwill, Nonlinear programing via penalty functions, Manag. Sci. 13 (1967) 344–358.
[38] I. Zang, A smoothing out technique for min-max optimization, Math. Program. 19 (1980) 61–77.
)