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

@article{Kawasaki1988AnEE,
  title={An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems},
  author={Hidefumi Kawasaki},
  journal={Mathematical Programming},
  year={1988},
  volume={41},
  pages={73-96}
}
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… CONTINUE READING

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