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Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps

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Abstract

In this paper, by using the notion of strong subdifferential and epsilon-subdifferential, necessary optimality conditions are established firstly for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector optimization problem, where its objective function and constraint set are denoted by using differences of two vector-valued maps, respectively. Then, by using the concept of approximate pseudo-dissipativity, sufficient optimality conditions are obtained. As an application of these results, sufficient and necessary optimality conditions are also given for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector fractional mathematical programming.

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Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (Grant number: 11171362) and the Natural Science Foundation Project of CQ CSTC (Grant number: cstc2012jjA00038). The authors thank the anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper.

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Authors and Affiliations

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

    X. L. Guo & S. J. Li

  2. College of Science, Henan Institute of Engineering, Zhengzhou, 451191, China

    X. L. Guo

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  1. X. L. Guo
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  2. S. J. Li
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Correspondence to S. J. Li.

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Communicated by Radu Ioan Bot.

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Guo, X.L., Li, S.J. Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps. J Optim Theory Appl 162, 821–844 (2014). https://doi.org/10.1007/s10957-013-0327-3

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  • DOI: https://doi.org/10.1007/s10957-013-0327-3

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