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Saddle Points and Pareto Points in Multiple Objective Programming

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Abstract

In this paper relationships between Pareto points and saddle points are studied in convex and nonconvex multiple objective programming. The analysis is based on partitioning the index sets of objectives and constraints and splitting the original problem into subproblems having a special structure. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. In the nonconvex case, a saddle point characterization of Pareto points is possible under assumptions that guarantee existence of Pareto points and stability conditions of single objective problems. Essentially, these conditions are not stronger than those in analogous results for single objective programming.

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Author information

Authors and Affiliations

  1. Department of Engineering Science, University of Auckland, Auckland, New Zealand

    Matthias Ehrgott

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Margaret M. Wiecek

Authors
  1. Matthias Ehrgott

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  2. Margaret M. Wiecek

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Corresponding author

Correspondence toMatthias Ehrgott.

Additional information

This research was partially supported by ONR Grant N00014-97-1-784

AMS Subject Classification: 90C29, 90C26

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