Abstract
The study of epsilon solutions in vector optimization problems was started in 1979 by S. S. Kutateladze [1]. These types of solutions are interesting because of their relation to non-differentiable optimization and the vector valued extensions of Ekeland’s variational principle as considered by P. Loridan [2] and I. Vályi [3], but computational aspects are perhaps even more important. In practical situations, namely, we often stop the calculations at values that we consider sufficiently close to the optimal solution, or use algorithms that result in some approximates of the Pareto set. Such procedures can result in epsilon solutions that are under study in this paper. A paper by D. J. White [4] deals with this issue and investigates how well these solutions approximate the exact solutions.
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References
KUTATELADZE, S.S., Convex ε-Programming, Soviet Mathematical Dokiady, Vol. 20, No. 2, pp. 391–393, 1979.
LORIDAN P., ε-Solutions in Vector Minimization Problems, Journal of Optimization Theory and Applications, Vol. 43, No. 2, pp. 265–276, 1984.
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VALYI I., Strict Approximate Duality in Vector Spaces, optimization, (to appear).
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© 1987 Springer-Verlag Berlin Heidelberg
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Vályi, I. (1987). Epsilon Solutions and Duality in Vector Optimization. In: Sawaragi, Y., Inoue, K., Nakayama, H. (eds) Toward Interactive and Intelligent Decision Support Systems. Lecture Notes in Economics and Mathematical Systems, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46607-6_45
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DOI: https://doi.org/10.1007/978-3-642-46607-6_45
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