Saddle points and Pareto points in multiple objective programming

Saddle points and Pareto points in multiple objective programming

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Article ID: iaor2006367
Country: Germany
Volume: 32
Issue: 1
Start Page Number: 11
End Page Number: 33
Publication Date: May 2005
Journal: Journal of Global Optimization
Authors: ,
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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