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

Kely Diana Villacorta(kelydvv***at***ci.ufpb.br)
Paulo Roberto Oliveira(poliveir***at***cos.ufrj.br)
Antoine Soubeyran(antoine.soubeyran***at***gmail.com)

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 by \citet{conn} 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: trust-region methods, unconstrained multiobjective problem, Pareto critical point, satisficing process, worthwhile change,variational rationality

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Applications -- OR and Management Sciences

Category 3: Nonlinear Optimization


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Entry Submitted: 05/19/2013
Entry Accepted: 05/28/2013
Entry Last Modified: 05/19/2013

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