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Local structure of feasible sets in nonlinear programming, part I: Regularity

Part of the Lecture Notes in Mathematics book series (LNM,volume 1005)

Abstract

Given a feasible point for a nonlinear programming problem, we investigate the structure of the feasible set near that point. Under the constraint qualification called regularity, we show how to compute the tangent cone to the feasible set, and to produce feasible arcs with prescribed first and second derivatives. In order to carry out these constructions, we show that a particular way of representing the feasible set (as a system of equations with constrained variables) is particularly useful. We also give fairly short proofs of the first-order and second-order necessary optimality conditions in very general forms, using the arc constructions mentioned above.

Keywords

  • Nonlinear Programming
  • Regular Point
  • Tangent Cone
  • Constraint Qualification
  • Nonlinear Programming Problem

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References

  1. O. L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Anal. Appl. 17 (1967), pp. 37–47.

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© 1983 Springer-Verlag

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Robinson, S.M. (1983). Local structure of feasible sets in nonlinear programming, part I: Regularity. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112538

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  • DOI: https://doi.org/10.1007/BFb0112538

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12334-7

  • Online ISBN: 978-3-540-40967-0

  • eBook Packages: Springer Book Archive