Abstract
A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602–626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.
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The authors are grateful to the anonymous reviewers, whose comments improved this work.
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This work has been partially supported by Universidad Nacional del Sur, Project 24/L082.
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Carrizo, G.A., Lotito, P.A. & Maciel, M.C. Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem. Math. Program. 159, 339–369 (2016). https://doi.org/10.1007/s10107-015-0962-6
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DOI: https://doi.org/10.1007/s10107-015-0962-6