An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems

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Abstract

A group of curves generates a new curve which is called an envelope. When one deals with a minimization problem with infinitely many inequality constraints, one must encounter an envelopelike effect caused by the constraints. In this paper we present second-order necessary conditions, which involve a new term besides the second derivative of the Lagrange function. We apply our results to minimizing problems of sup-type functions. One will observe in examples that the new term given in this paper explains well the behavior of the second directional derivative of the sup-type function.

Original languageEnglish
Pages (from-to)73-96
Number of pages24
JournalMathematical Programming
Volume41
Issue number1-3
DOIs
Publication statusPublished - May 1 1988

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Second-order Necessary Conditions
Inequality Constraints
Minimization Problem
Envelope
Second derivative
Derivatives
Curve
Directional derivative
Term
Lagrange
Inequality constraints

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

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