Article ID: | iaor19921171 |
Country: | Netherlands |
Volume: | 49 |
Issue: | 2 |
Start Page Number: | 213 |
End Page Number: | 229 |
Publication Date: | Dec 1990 |
Journal: | Mathematical Programming |
Authors: | Kawasaki H. |
Keywords: | semi-infinite programming |
The second derivative of an envelope cannot be expressed only by second derivatives of the constituent functions. By taking account of this fact, the paper derives new second order necessary optimality conditions for minimization of a sup-type function. The conditions involve an extra term besides the second derivative of the Lagrange function. Furthermore, comment will be made on the relationship between the extra term and a kind of second order directional derivative of the sup-type function.