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Extrema Constrained by a Family of Curves and Local Extrema

Author

Listed:
  • O. Dogaru

    (Polytechnic University of Bucharest)

  • I. Ţevy

    (Polytechnic University of Bucharest)

  • C. Udrişte

    (Polytechnic University of Bucharest)

Abstract

This paper considers the connections between the local extrema of a function f:D→R and the local extrema of the restrictions of f to specific subsets of D. In particular, such subsets may be parametrized curves, integral manifolds of a Pfaff system, Pfaff inequations. The paper shows the existence of C 1 or C 2-curves containing a given sequence of points. Such curves are then exploited to establish the connections between the local extrema of f and the local extrema of f constrained by the family of C 1 or C 2-curves. Surprisingly, what is true for C 1-curves fails to be true in part for C 2-curves. Sufficient conditions are given for a point to be a global minimum point of a convex function with respect to a family of curves.

Suggested Citation

  • O. Dogaru & I. Ţevy & C. Udrişte, 1998. "Extrema Constrained by a Family of Curves and Local Extrema," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 605-621, June.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:3:d:10.1023_a:1022642126176
    DOI: 10.1023/A:1022642126176
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