Optimality conditions in nonconical multiple-objective programming

  • G. B. Hazen
  • T. L. Morin
Contributed Papers


Previous theoretical work in multiple-objective optimization has focused entirely on vector orders representable by positive cones. Here, we treat multiple-objective problems in which solutions are sought which are maximal (efficient, nondominated) under an order which may be nonconical. Compactness conditions under which maximal solutions exist and bound the remaining alternatives are given. First-order necessary conditions and first-order sufficient conditions for maximality in general normed linear spaces are derived, and a scalarization result is given. A small computational example is also presented. Several previous results are special cases of those given here.

Key Words

Multiple-objective optimization vector optimization existence theorems first-order optimality conditions normed linear spaces 


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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • G. B. Hazen
    • 1
  • T. L. Morin
    • 2
  1. 1.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanston
  2. 2.School of Industrial EngineeringPurdue UniversityWest Lafayette

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