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Uniqueness conditions for Kuhn-Tucker points on a disk

Abstract

Consider minimizingf onD which is diffeomorphic to a disk. Under a genericity assumption, the number of points onD satisfying the Kuhn-Tucker necessary conditions for minimum is odd. We give conditions which imply that a local minimum is global and a necessary and sufficient condition that a Kuhn-Tucker point is the solution. Convex transformable problems satisfy the latter condition.D may be of full dimension or be embedded on a manifold or it may be given by a system of concave inequalities.

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Additional information

The work on which this paper is based was done while the author was visiting the Group for the Application of Mathematics and Statistics to Economics at the University of California, Berkeley, Spring 1981. The author would like to thank the Group, and Professor G. Debreu in particular, for the hospitality. He benefited from discussions with Professors S. Smale, A. Mas-Colell, K. Nishimura, and L. Chenault, among others. He also wishes to thank two referees of this journal for helpful comments.

Communicated by M. Avriel

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Yun, K.K. Uniqueness conditions for Kuhn-Tucker points on a disk. J Optim Theory Appl 44, 701–721 (1984). https://doi.org/10.1007/BF00938403

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Key Words

  • Kuhn-Tucker points
  • local and global minima
  • nonlinear programming
  • Morse functions
  • convex transformable programs