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

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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
Volume49
Issue number2
Publication statusPublished - Dec 1990

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Second-order Optimality Conditions
Necessary Optimality Conditions
Second derivative
Derivatives
Directional derivative
Second-order Derivatives
Term
Lagrange
Envelope
Optimality conditions

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design
  • Software
  • Management Science and Operations Research
  • Safety, Risk, Reliability and Quality
  • Mathematics(all)
  • Applied Mathematics

Cite this

Second order necessary optimality conditions for minimizing a sup-type function. / Kawasaki, Hidefumi.

In: Mathematical Programming, Vol. 49, No. 2, 12.1990, p. 213-229.

Research output: Contribution to journalArticle

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