| Issue |
Int. J. Simul. Multidisci. Des. Optim.
Volume 10, 2019
|
|
|---|---|---|
| Article Number | A10 | |
| Number of page(s) | 7 | |
| DOI | https://doi.org/10.1051/smdo/2019010 | |
| Published online | 07 June 2019 | |
Research Article
Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem
1
School of Mathematical Sciences,
Main Campus, USM,
11800
Geligor,
Pulau Penang,
Malaysia
2
Department of Mathematics, Yusuf Maitama Sule University, Kano,
700241
Kabuga,
Kano,
Nigeria
* e-mail: mansurkust@yahoo.com
Received:
1
November
2018
Accepted:
13
May
2019
In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.
Key words: Courant-Beltrami penalty function / penalized problem / Lagrangian dual
© M. Hassan and A. Baharum, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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