کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4629243 | 1340575 | 2013 | 10 صفحه PDF | دانلود رایگان |

In this paper, we extend the concepts of linearizing cone, regularity assumption and Lagrange multiplier rule due to Maurer and Zowe [H. Maurer, J. Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Program. 16 (1979) 98–110] to an optimization problem under inclusion constraints. By virtue of the Robinson–Ursescu open mapping theorem, we obtain a Kuhn–Tucker necessary optimality condition. Moreover, we propose a Lagrangian by using the support function for set-valued maps, and establish some second-order sufficient and necessary optimality conditions for a strict local minimizer of order 2 based on the second-order derivative of the Lagrangian. As applications, we also investigate some second-order optimality conditions for the strict local minimizer of order 2 of a smooth scalar optimization problem with equality and inequality constraints.
Journal: Applied Mathematics and Computation - Volume 219, Issue 9, 1 January 2013, Pages 4816–4825