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Efficient and weakly efficient solutions for the vector topical optimization

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Abstract

In this paper, we consider some scalarization functions, which consist of the generalized min-type function, the so-called plus-Minkowski function and their convex combinations. We investigate the abstract convexity properties of these scalarization functions and use them to identify the maximal points of a set in an ordered vector space. Then, we establish some versions of Farkas type results for the infinite inequality system involving vector topical functions. As applications, we obtain the necessary and sufficient conditions of efficient solutions and weakly efficient solutions for a vector topical optimization problem, respectively.

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Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (Grant Numbers: 11571055, 11171362) and Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant Number: KJ1501503).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    C. L. Yao & S. J. Li

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  1. C. L. Yao
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  2. S. J. Li
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Correspondence to S. J. Li.

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Yao, C.L., Li, S.J. Efficient and weakly efficient solutions for the vector topical optimization. Optim Lett 12, 1929–1945 (2018). https://doi.org/10.1007/s11590-017-1193-y

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