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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This research was partially supported by ONR Grant N00014-97-1-784
AMS Subject Classification: 90C29, 90C26
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Ehrgott, M., Wiecek, M.M. Saddle Points and Pareto Points in Multiple Objective Programming. J Glob Optim 32, 11–33 (2005). https://doi.org/10.1007/s10898-004-5902-6
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DOI: https://doi.org/10.1007/s10898-004-5902-6