Abstract
The paper contains definitions of different types of nondominated approximate solutions to vector optimization problems and gives some of their elementary properties. Then, saddle-point theorems corresponding to these solutions are presented with an application relative to approximate primal-dual pairs of solutions.
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Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 31, pp. 509–529, 1980.
Corley, H. W.,Duality Theory with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560–568, 1981.
Loridan, P.,ε-Solutions in Vector Minimization Problems, Journal of Optimization Theory and Applications, Vol. 43, pp. 265–276, 1984.
Strodiot, J. J., Nguyen, V. H., andHeukemes, N.,ε-Optimal Solutions in Nondifferentiable Convex Programming and Some Related Questions, Mathematical Programming, Vol. 25, pp. 307–328, 1983.
Kutateladze, S. S.,ε-Subdifferentials and ε-Optimality, Sibirskii Matematicheskii Zhurnal, Vol. 21, pp. 120–130, 1980 (in Russian).
Peressini, A. L.,Ordered Topological Vector Spaces, Harper and Row, New York, New York, 1967.
Holmes, R. B.,Geometric Functional Analysis, Springer, Berlin, Germany, 1975.
Zowe, J.,Konvexe Funktionen und Konvexe Dualitätstheorie in Geordneten Vektorräumen, Habilitationsschrift dem Naturwissenschaftlichen Fachbereich IV der Bayerischen Julius-Maximilians-Universität Würzburg, Würzburg, Germany, 1976.
Vályi, I.,On Duality Theory Related to Approximate Solutions of Vector Optimization Problems, Nondifferentiable Optimization: Motivations and Applications, Edited by V. F. Demyanov and D. Pallaschke, Springer, Berlin, Germany, 1985.
Köthe, G.,Topologische Lineare Räume, I, Springer, Berlin, Germany, 1966.
Luc, D. T.,On Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 43, pp. 557–582, 1984.
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Communicated by P. L. Yu
This research was carried out while the author was working at the Bureau for Systems Analysis, State Office for Technical Development, Budapest, Hungary. The author is indebted to the referees for their useful comments.
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Vályi, I. Approximate saddle-point theorems in vector optimization. J Optim Theory Appl 55, 435–448 (1987). https://doi.org/10.1007/BF00941179
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DOI: https://doi.org/10.1007/BF00941179