Article ID: | iaor20134146 |
Volume: | 56 |
Issue: | 4 |
Start Page Number: | 1463 |
End Page Number: | 1499 |
Publication Date: | Aug 2013 |
Journal: | Journal of Global Optimization |
Authors: | Deb Kalyanmoy, Dutta Joydeep, Tulshyan Rupesh, Arora Ramnik |
Keywords: | approximation, KarushKuhnTucker (KKT) |
Karush–Kuhn–Tucker (KKT) optimality conditions are often checked for investigating whether a solution obtained by an optimization algorithm is a likely candidate for the optimum. In this study, we report that although the KKT conditions must all be satisfied at the optimal point, the extent of violation of KKT conditions at points arbitrarily close to the KKT point is not smooth, thereby making the KKT conditions difficult to use directly to evaluate the performance of an optimization algorithm. This happens due to the requirement of complimentary slackness condition associated with KKT optimality conditions. To overcome this difficulty, we define modified