A Spectral Approach to Solve Box-constrained Multi-objective Optimization Problems

This paper presents some first and second order conditions necessary for the Pareto optimality of box-constrained multi-objective optimization problems. These necessary conditions are related to the spectrum of a matrix defined via the gradient vectors and the Hessian matrices of the objective functions. These necessary conditions are used to develop two algorithms. The first one is built taking into account the first order necessary conditions and determines some critical points for the multi-objective problems considered. The second one is based on the second order necessary conditions and discards the critical points that do not belong to the local Pareto optimal front. Some numerical results are shown.

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