Abstract
We consider a Pareto multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and inequality constraints are locally Lipschitz, and the equality constraints are Fréchet differentiable. We study several constraint qualifications in the line of Maeda (J. Optim. Theory Appl. 80: 483–500, 1994) and, under the weakest ones, we establish strong Kuhn–Tucker necessary optimality conditions in terms of Clarke subdifferentials so that the multipliers of the objective functions are all positive.
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This work was supported (for the second and third authors) by the Spanish Ministry of Education and Science under projects MTM2006-02629 and Ingenio Mathematica (i-MATH) CSD2006-00032 (Consolider-Ingenio 2010), and moreover, for the second author, by the Consejería de Educación de la Junta de Castilla y León (Spain), project VA027B06. The authors are grateful to the anonymous referees for their valuable comments and suggestions.
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Giorgi, G., Jiménez, B. & Novo, V. Strong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems. TOP 17, 288–304 (2009). https://doi.org/10.1007/s11750-008-0058-z
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DOI: https://doi.org/10.1007/s11750-008-0058-z
Keywords
- Multiobjective optimization problems
- Constraint qualification
- Necessary conditions for Pareto minimum
- Lagrange multipliers
- Clarke subdifferential