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A Note on Multiobjective Optimization and Complementarity Constraints

Sven Leyffer (leyffer***at***mcs.anl.gov)

Abstract: We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set of Pareto points, and the objective maximizes some quality measure of this discrete set. We present encouraging numerical experience on a range of test problem collected from the literature.

Keywords: Multiobjective optimization, nonlinear programming, complementarity constraints, mathematical program with complementarity constraints

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Complementarity and Variational Inequalities

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: ANL/MCS-P1290-0905, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL 60439, September 2005

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Entry Submitted: 09/19/2005
Entry Accepted: 09/23/2005
Entry Last Modified: 09/19/2005

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