Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions
In this paper, we have reviewed some penalty function methods for solving constrained optimization problems in the literature and proposed a continuously differentiable logarithmic penalty function which consists of the proposed logarithmic penalty function and modified Courant-Beltrami penalty func...
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Online Access: | http://dx.doi.org/10.1080/25765299.2019.1600317 |
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doaj-35b731f6a2a74ecf846e72a71722c2da2020-11-25T02:50:48ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992019-01-0126120221410.1080/25765299.2019.16003171600317Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functionsMansur Hassan0Adam Baharum1Universiti Sains MalaysiaUniversiti Sains MalaysiaIn this paper, we have reviewed some penalty function methods for solving constrained optimization problems in the literature and proposed a continuously differentiable logarithmic penalty function which consists of the proposed logarithmic penalty function and modified Courant-Beltrami penalty function for equality and inequality constraints, respectively. Furthermore, we hybridized the two and came up with the general form of both (equality and inequality) constraints. However, in the first part, the equivalence between the sets of optimal solutions in the original optimization problem and its associated penalized logarithmic optimization problem constituted by invex functions with equality and inequality constraints has been established. In the second part, we have validated the general form of the logarithmic penalty function and compared the results with absolute value penalty function results by solving nine small problems from Hock-Schittkowski collections of test problems with different classifications. The experiments were carried out via quasi-newton algorithm using a fminunc routine function in matlab2018a. The general form yields a better objective value compared to absolute value penalty function.http://dx.doi.org/10.1080/25765299.2019.1600317penalty functionpenalized optimization problemlogarithmic penalty functioninvex functioncourant-beltrami penalty function |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mansur Hassan Adam Baharum |
spellingShingle |
Mansur Hassan Adam Baharum Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions Arab Journal of Basic and Applied Sciences penalty function penalized optimization problem logarithmic penalty function invex function courant-beltrami penalty function |
author_facet |
Mansur Hassan Adam Baharum |
author_sort |
Mansur Hassan |
title |
Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
title_short |
Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
title_full |
Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
title_fullStr |
Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
title_full_unstemmed |
Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
title_sort |
generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions |
publisher |
Taylor & Francis Group |
series |
Arab Journal of Basic and Applied Sciences |
issn |
2576-5299 |
publishDate |
2019-01-01 |
description |
In this paper, we have reviewed some penalty function methods for solving constrained optimization problems in the literature and proposed a continuously differentiable logarithmic penalty function which consists of the proposed logarithmic penalty function and modified Courant-Beltrami penalty function for equality and inequality constraints, respectively. Furthermore, we hybridized the two and came up with the general form of both (equality and inequality) constraints. However, in the first part, the equivalence between the sets of optimal solutions in the original optimization problem and its associated penalized logarithmic optimization problem constituted by invex functions with equality and inequality constraints has been established. In the second part, we have validated the general form of the logarithmic penalty function and compared the results with absolute value penalty function results by solving nine small problems from Hock-Schittkowski collections of test problems with different classifications. The experiments were carried out via quasi-newton algorithm using a fminunc routine function in matlab2018a. The general form yields a better objective value compared to absolute value penalty function. |
topic |
penalty function penalized optimization problem logarithmic penalty function invex function courant-beltrami penalty function |
url |
http://dx.doi.org/10.1080/25765299.2019.1600317 |
work_keys_str_mv |
AT mansurhassan generalizedlogarithmicpenaltyfunctionmethodforsolvingsmoothnonlinearprogramminginvolvinginvexfunctions AT adambaharum generalizedlogarithmicpenaltyfunctionmethodforsolvingsmoothnonlinearprogramminginvolvinginvexfunctions |
_version_ |
1724736271917514752 |