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Journal of Optimization Theory and Applications

, Volume 4, Issue 6, pp 394–412 | Cite as

Some duality relationships for the generalized Neyman-Pearson problem

  • Richard L. Francis
  • Gordon P. Wright
Contributed Papers

Abstract

In 1963, Kuhn presented a dual problem to a relatively well-known location problem, variously referred to as the generalized Fermat problem and the Steiner-Weber problem. The purpose of this paper is to point out how Kuhn's results can be adapted to provide a dual to the generalized Neyman-Pearson problem, a problem of fundamental interest in statistics, which has applications in control theory and a number of other areas. The Neyman-Pearson problem, termed the dual problem, is a constrained maximization problem and may be considered to be a calculus-of-variations analog to the bounded-variable problem of linear programming. When the dual problem has equality constraints, the primal problem is an unconstrained minimization problem. Duality results are also obtained for the case where the dual problem has inequality constraints.

Keywords

Control Theory Minimization Problem Equality Constraint Fermat Location Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • Richard L. Francis
    • 1
  • Gordon P. Wright
    • 2
  1. 1.Department of Industrial EngineeringThe Ohio State UniversityColumbus
  2. 2.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanston

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