How to cite this paper
Hassan, M & Baharum, A. (2019). A new logarithmic penalty function approach for nonlinear constrained optimization problem.Decision Science Letters , 8(3), 353-362.
Refrences
Antczak, T. (2009). Exact penalty functions method for mathematical programming problems involving invex functions. European Journal of Operational Research, 198(1), 29–36.
Antczak, T. (2011). The l_1 exact G -penalty function method and G -invex mathematical programming problems. Mathematical and Computer Modelling, 54(9–10), 1966–1978.
Antczak, T. (2010). The L 1 Penalty Function Method For Nonconvex Differentiable Optimization Problems With Inequality Constraints. Asia-Pacific Journal of Operational Research, 27(05), 559–576.
Bazaraa, M., Sherali, H., & Shetty, C.(2006). Nonlinear Programming: theory and algorithm. Wiley Interscience, A John Wiley & Sons,INC., Publication.
Chen, Z., & Dai, Y. H. (2016). A line search exact penalty method with bi-object strategy for nonlinear constrained optimization. Journal of Computational and Applied Mathematics, 300, 245–258.
Dolgopolik, M. V. (2018). A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness. Journal of Optimization Theory and Applications, 176(3), 728–744.
Echebest, N., Sánchez, M. D., & Schuverdt, M. L. (2016). Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function. Journal of Optimization Theory and Applications, 168(1), 92–108.
Ernst, E., & Volle, M. (2013). Generalized Courant-Beltrami penalty functions and zero duality gap for conic convex programs. Positivity, 17(4), 945–964.
Hock, W., & Schittkowski, K. (1981). Test Examples for Nonlinear Programming codes. Berlin: Lecture Note in Economics and Mathematical System, Springer-Verl.
Jayswal, A., & Choudhury, S. (2014). Convergence of exponential penalty function method for multiobjective fractional programming problems. Ain Shams Engineering Journal, 5(4), 1371–1376.
Lin, Q., Loxton, R., Teo, K. L., Wu, Y. H., & Yu, C. (2014). A new exact penalty method for semi-infinite programming problems. Journal of Computational and Applied Mathematics, 261, 271–286.
Liu, S., & Feng, E. (2010). The exponential penalty function method for multiobjective programming problems. Optimization Methods and Software, 25(5), 667–675.
Mangasarian, O. L. (1985). Sufficiency of Exact Penalty Minimization. {SIAM} Journal on Control and Optimization, 23(1), 30–37.
Morrison, D. D. (1968). Optimization by Least Squares. SIAM Journal on Numerical Analysis, 5(1), 83–88.
Utsch De Freitas Pinto, R. L., & Martins Ferreira, R. P. (2014). An exact penalty function based on the projection matrix. Applied Mathematics and Computation, 245, 66–73.
Venkata Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7(1), 19–34.
Zangwill. (1967). Nonlinear programming via penalty functions. Management Science, 13(5), 344–358.
Antczak, T. (2011). The l_1 exact G -penalty function method and G -invex mathematical programming problems. Mathematical and Computer Modelling, 54(9–10), 1966–1978.
Antczak, T. (2010). The L 1 Penalty Function Method For Nonconvex Differentiable Optimization Problems With Inequality Constraints. Asia-Pacific Journal of Operational Research, 27(05), 559–576.
Bazaraa, M., Sherali, H., & Shetty, C.(2006). Nonlinear Programming: theory and algorithm. Wiley Interscience, A John Wiley & Sons,INC., Publication.
Chen, Z., & Dai, Y. H. (2016). A line search exact penalty method with bi-object strategy for nonlinear constrained optimization. Journal of Computational and Applied Mathematics, 300, 245–258.
Dolgopolik, M. V. (2018). A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness. Journal of Optimization Theory and Applications, 176(3), 728–744.
Echebest, N., Sánchez, M. D., & Schuverdt, M. L. (2016). Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function. Journal of Optimization Theory and Applications, 168(1), 92–108.
Ernst, E., & Volle, M. (2013). Generalized Courant-Beltrami penalty functions and zero duality gap for conic convex programs. Positivity, 17(4), 945–964.
Hock, W., & Schittkowski, K. (1981). Test Examples for Nonlinear Programming codes. Berlin: Lecture Note in Economics and Mathematical System, Springer-Verl.
Jayswal, A., & Choudhury, S. (2014). Convergence of exponential penalty function method for multiobjective fractional programming problems. Ain Shams Engineering Journal, 5(4), 1371–1376.
Lin, Q., Loxton, R., Teo, K. L., Wu, Y. H., & Yu, C. (2014). A new exact penalty method for semi-infinite programming problems. Journal of Computational and Applied Mathematics, 261, 271–286.
Liu, S., & Feng, E. (2010). The exponential penalty function method for multiobjective programming problems. Optimization Methods and Software, 25(5), 667–675.
Mangasarian, O. L. (1985). Sufficiency of Exact Penalty Minimization. {SIAM} Journal on Control and Optimization, 23(1), 30–37.
Morrison, D. D. (1968). Optimization by Least Squares. SIAM Journal on Numerical Analysis, 5(1), 83–88.
Utsch De Freitas Pinto, R. L., & Martins Ferreira, R. P. (2014). An exact penalty function based on the projection matrix. Applied Mathematics and Computation, 245, 66–73.
Venkata Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7(1), 19–34.
Zangwill. (1967). Nonlinear programming via penalty functions. Management Science, 13(5), 344–358.