Nonlinear constrained optimizer and parallel processing for golden block line search
Abstract
Generalized exponential penalty functions are constructed for the multiplier methods in solving nonlinear programming problems. The non-smooth extreme constraint Gext is replaced by a single smooth constraint Gs by using the generalized exponential function (base a > 1). The well-known K.S. function is found to be a special case of our proposed formulation . Parallel processing for Golden block line search algorithm is then summarized, which can also be integrated into our formulation. Both small and large-scale nonlinear programming problems (up to 2000 variables and 2000 nonlinear constraints) have been solved to validate the proposed algorithms.
References
[1] G. Kreisselmeier, R. Steinhauser. Systematic control design by optimizing a vector performance index. Proc. IFAC Symp. on Computer Aided Design of Control System. Zurich, Switzerland, 1979.
[2] G.P. McCormick. Nonlinear Programming, Theory, Algorithm, and Applications. John Wiley and Sons, New York, 1983.
[3] M.J.D. Powell. A method for nonlinear constraints in minimization problems. In: R. Fletcher, ed. , Optimization, 283- 298. Academic, London, 1969.
[4] M.R. Hestenes. Multiplier and gradient methods. J. Optim. Theor. Appl., 4(5): 303- 320, 1969.
[5] A.B. Templeman, X.S. Li. A maximum entropy approach to constrained non-linear programming. Eng. Optimization, 12: 191- 205 , 1987.
[2] G.P. McCormick. Nonlinear Programming, Theory, Algorithm, and Applications. John Wiley and Sons, New York, 1983.
[3] M.J.D. Powell. A method for nonlinear constraints in minimization problems. In: R. Fletcher, ed. , Optimization, 283- 298. Academic, London, 1969.
[4] M.R. Hestenes. Multiplier and gradient methods. J. Optim. Theor. Appl., 4(5): 303- 320, 1969.
[5] A.B. Templeman, X.S. Li. A maximum entropy approach to constrained non-linear programming. Eng. Optimization, 12: 191- 205 , 1987.
Published
2023-05-22
Issue
pp. 469-477
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Nguyen, D. T., Tang, W. H., Tung, Y. K., & Runesha, H. B. (2023). Nonlinear constrained optimizer and parallel processing for golden block line search. Computer Assisted Methods in Engineering and Science, 6(3-4), 469-477. https://cames3.ippt.pan.pl/index.php/cames/article/view/1308
