Name
Abstract | ||
|---|---|---|
In this paper, we study first- and second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subderivative of the penalty term, we also present sufficient conditions for a penalty term to be of KKT-type. We then derive a second-order necessary condition by assuming a second-order constraint qualification, which requires that the second-order linearized tangent set is included in the closed convex hull of the kernel of the parabolic subderivative of the penalty term. In particular, for a penalty term with order $$\\frac{2}{3}$$23, by assuming the nonpositiveness of a sum of a second-order derivative and a third-order derivative of the original data and applying a third-order Taylor expansion, we obtain the second-order necessary condition. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s10957-014-0664-x | J. Optimization Theory and Applications |
Keywords | Field | DocType |
subderivative,kkt condition | Mathematical optimization,Mathematical analysis,Nonlinear programming,Convex hull,Subderivative,Tangent,Karush–Kuhn–Tucker conditions,Mathematics,Parabola,Penalty method,Taylor series | Journal |
Volume | Issue | ISSN |
165 | 3 | 1573-2878 |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| K. W. Meng | 1 | 13 | 2.41 |
| Xiaoqi Yang | 2 | 126 | 20.85 |