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Steepest descent methods for multicriteria optimization. (English) Zbl 1054.90067
Summary: We propose a steepest descent method for unconstrained multicriteria 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.

MSC:
90C29 Multi-objective and goal programming
90C52 Methods of reduced gradient type
Software:
NIMBUS
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