Abstract
In this paper, we introduce a definition of generalized convexlike functions (preconvexlike functions). Then, under the weakened convexity, we study vector optimization problems in Hausdorff topological linear spaces. We establish some generalized Motzkin theorems of the alternative. By use of these theorems of the alternative, we obtain some Lagrangian multiplier theorems. A saddle-point theorem and a scalarization theorem are also derived.
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Communicated by F. Giannessi
The author thank Ginndomenico Mastrocni for helpful and useful comments.
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Zeng, R., Caron, R.J. Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems. J Optim Theory Appl 131, 281–299 (2006). https://doi.org/10.1007/s10957-006-9140-6
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DOI: https://doi.org/10.1007/s10957-006-9140-6