Extrema Constrained by a Family of Curves and Local Extrema |
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Authors: | Dogaru O. Ţevy I. Udrişte C. |
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Affiliation: | (1) Department of Mathematics I, Polytechnic University of Bucharest, Bucharest, Romania |
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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 C1 or C2-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 C1 or C2-curves. Surprisingly, what is true for C1-curves fails to be true in part for C2-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. |
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Keywords: | Minima constrained by Ck-curves Ck-curves defined by sequences convexity extrema |
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