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

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The second derivative of an envelope cannot be expressed only by second derivatives of the constituent functions. By taking account of this fact, we derive 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, we will comment on the relationship between the extra term and a kind of second order directional derivative of the sup-type function.

Original languageEnglish
Pages (from-to)213-229
Number of pages17
JournalMathematical Programming, Series B
Issue number2
Publication statusPublished - Dec 1 1990


All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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