A Note on Multiobjective Optimization and Complementarity Constraints

Published: 2005/09/19

Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Multi-Criteria Optimization complementarity constraints, mathematical program with complementarity constraints, multiobjective optimization, nonlinear programming Short URL: https://optimization-online.org/?p=9017

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.

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

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