Steepest descent methods for multicriteria optimization

Steepest descent methods for multicriteria optimization

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Article ID: iaor20013639
Country: Germany
Volume: 51
Issue: 3
Start Page Number: 479
End Page Number: 494
Publication Date: Jan 2000
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors:
Abstract:

We propose a steepest descent method for unconstrained multi-criteria optimization and a ‘feasible descent direction’ method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuously differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuously differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto optimality. Both methods do not scalarize the original vector optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the steepest descent method and Zoutendijk's method of feasible directions, respectively.

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