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Generalized tangent cone and an optimization problem in a normed space

Abstract

Most abstract multiplier rules in the literature are based on the tangential approximation at a point to some set in a Banach space. The present paper is concerned with the study of a generalized tangent cone, which is a tangential approximation to that set at a common point of two sets. The new notion of tangent cone generalizes previous concepts of tangent cones. This generalized tangent cone is used to characterize the optimality conditions for a simultaneous maximization and minimization problem. The paper is of theoretical character; practical applications are not found so far.

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Communicated by P. Varaiya

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Dancs, S. Generalized tangent cone and an optimization problem in a normed space. J Optim Theory Appl 67, 43–55 (1990). https://doi.org/10.1007/BF00939734

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Key Words

  • Optimization theory
  • tangent cones
  • contingent cones
  • necessary conditions
  • abstract multiplier rules