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First-order and second-order ε-directional derivatives of a marginal function in convex programming with linear inequality constraints

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Abstract

Hiriart-Urruty gave formulas of the first-order and second-order ε-directional derivatives of a marginal function for a convex programming problem with linear equality constraints, that is, the image of a function under linear mapping (Ref. 1). In this paper, we extend his results to a problem with linear inequality constraints. The formula of the first-order derivative is given with the help of a duality theorem. A lower estimate for the second-order ε-directional derivative is given.

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References

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Additional information

The author wishes to thank Professor N. Furukawa and Dr. H. Kawasaki for their helpful comments and encouragements. He is also indebted to one referee for pointing out the proof of Proposition 3.1.

Communicated by A. V. Fiacco

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Shiraishi, S. First-order and second-order ε-directional derivatives of a marginal function in convex programming with linear inequality constraints. J Optim Theory Appl 66, 489–502 (1990). https://doi.org/10.1007/BF00940934

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Key Words

  • Convex programming
  • marginal function
  • duality theorem
  • first-order and second-order ε-directional derivatives