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ε-solutions in vector minimization problems

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Abstract

This paper presents some properties of ε-solutions for vector minimization problems where the function to be optimized takes its values in the Euclidean space ℝp. The results obtained generalize the classical ones for exact Pareto solutions.

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References

  1. Tanino, T., andSawaragi, Y.,Conjugate Maps and Duality in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 31, No. 4, 1980.

  2. Kutateladze, S. S.,Convex ε-Programming, Soviet Mathematics Doklady, Vol. 20, No. 2, 1979.

  3. Loridan, P.,Necessary Conditions for ε-Optimality, Mathematical Programming Study 19, 1982.

  4. Strodiot, J. J., Nguyen, V. H., andHeukenes, N.,ε-Optimal Solutions in Nondifferentiable Convex Programming and Some Related Questions, Facultés Universitaires de Namur, Namur, Belgium, Report No. 80/12, 1980.

    Google Scholar 

  5. Ben-Tal, A.,Characterization of Pareto and Lexicographic Optimal Solutions, Springer-Verlag, New York, New York, 1980.

    Google Scholar 

  6. Fogelman-Soulie, F., andMoulin, H.,La Convexité dans les Mathématiques de la Décision, Hermann, Paris, France, 1979.

    Google Scholar 

  7. Ekeland, I.,On the Variational Principle, Journal of Mathematical Analysis and Applications, Vol. 47, No. 2, 1974.

  8. Ekeland, I., andTemam, R.,Analyse Convexe et Problèmes Variationnels, Dunod, Paris, France, 1974.

    Google Scholar 

  9. Clarke, F. H.,A New Approach to Lagrange Multipliers, Mathematics of Operations Research, Vol. 1, No. 2, 1976.

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Communicated by G. Leitmann

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Loridan, P. ε-solutions in vector minimization problems. J Optim Theory Appl 43, 265–276 (1984). https://doi.org/10.1007/BF00936165

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  • DOI: https://doi.org/10.1007/BF00936165

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