Second order necessary optimality conditions for minimizing a sup-type function

Second order necessary optimality conditions for minimizing a sup-type function

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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:
Keywords: semi-infinite programming
Abstract:

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.

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