A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

Kelyd.V. Villacorta, Paulo R. Oliveira and Antoine Soubeyran

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Abstract: Multiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on "variational rationality" concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences.

Keywords: Pareto critical point; Satisficing process; Trust-region methods; Unconstrained multiobjective problem; Variational rationality; Worthwhile change (search for similar items in EconPapers)
Date: 2014-03
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Citations: View citations in EconPapers (7)

Published in Journal of Optimization Theory and Applications, 2014, 160 (3), pp.865--889. ⟨10.1007/s10957-013-0392-7⟩

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Journal Article: A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01463767

DOI: 10.1007/s10957-013-0392-7

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