Steepest descent methods for multicriteria optimization
Steepest descent methods for multicriteria optimization
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.
Multi-objective programming, Multicriteria optimization, Pareto points, Steepest descent, Vector optimization
479-494
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Svaiter, Benar Fux
ce91cd2a-d598-42f9-b8c9-1ddf56c3192d
August 2000
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Svaiter, Benar Fux
ce91cd2a-d598-42f9-b8c9-1ddf56c3192d
Fliege, Jörg and Svaiter, Benar Fux
(2000)
Steepest descent methods for multicriteria optimization.
Mathematical Methods of Operations Research, 51 (3), .
(doi:10.1007/s001860000043).
Abstract
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.
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Published date: August 2000
Keywords:
Multi-objective programming, Multicriteria optimization, Pareto points, Steepest descent, Vector optimization
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Local EPrints ID: 482538
URI: http://eprints.soton.ac.uk/id/eprint/482538
ISSN: 1432-2994
PURE UUID: 377e34b0-821f-41b8-8d2b-d7ccd33a3988
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Date deposited: 10 Oct 2023 16:47
Last modified: 18 Mar 2024 03:08
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Author:
Benar Fux Svaiter
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