Extrema Constrained by a Family of Curves and Local Extrema

O. Dogaru, I. Ţevy and C. Udrişte
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O. Dogaru: Polytechnic University of Bucharest
I. Ţevy: Polytechnic University of Bucharest
C. Udrişte: Polytechnic University of Bucharest

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 3, No 5, 605-621

Abstract: 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.

Keywords: Minima constrained by C k-curves; C k-curves defined by sequences; convexity; extrema (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022642126176

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