Saddle point criteria and duality in multiobjective programming via an eta-approximation method
- Autores: T. Antczak
- Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 47, Nº 2, 2005, págs. 155-172
- Idioma: inglés
- DOI: 10.1017/s1446181100009962
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Resumen
In this paper, Antczak's -approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the -saddle points of the associated -approximated vector optimisation problems. We introduce an -Lagrange function for a constructed -approximated vector optimisation problem and present some modified -saddle point results. Furthermore, we construct an -approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between -approximation vector optimisation problems and their duals (that is, an -approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.
