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Sequential Optimality Conditions for Fractional Optimization with Applications to Vector Optimization

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Abstract

In this paper, in the absence of any constraint qualifications, a sequential Lagrange multiplier rule condition characterizing optimality for a fractional optimization problem is obtained in terms of the \(\varepsilon \)-subdifferentials of the functions involved at the minimizer. The significance of this result is that it yields the standard Lagrange multiplier rule condition for the fractional optimization problem under a simple closedness condition that is much weaker than the well-known constraint qualifications. A sequential condition characterizing optimality involving only subdifferentials at nearby points to the minimizer is also investigated. As applications, the proposed approach is applied to investigate sequential optimality conditions for vector fractional optimization problems.

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Acknowledgments

We would like to express our sincere thanks to the anonymous referees for many helpful comments and constructive suggestions which have contributed to the final preparation of this paper. This research was partially supported by the National Natural Science Foundation of China (Grant Nos: 11301570 and 11001287), the Basic and Advanced Research Project of CQ CSTC (Grant No: cstc20 13jcyjA00003), the China Postdoctoral Science Foundation funded project (Grant No: 2013M540697) and the Natural Science Foundation Project of CQ CSTC (Grant No: cstc2012jjA00038).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing , 400067, China

    Xiang-Kai Sun & Xian-Jun Long

  2. College of Automation, Chongqing University, Chongqing , 400044, China

    Xiang-Kai Sun

  3. State Key Laboratory of Power Transmission Equipment and System Security and New Technology, College of Automation, Chongqing University, Chongqing , 400044, China

    Yi Chai

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  1. Xiang-Kai Sun
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  2. Xian-Jun Long
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Correspondence to Xiang-Kai Sun.

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Communicated by Harold P. Benson.

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Sun, XK., Long, XJ. & Chai, Y. Sequential Optimality Conditions for Fractional Optimization with Applications to Vector Optimization. J Optim Theory Appl 164, 479–499 (2015). https://doi.org/10.1007/s10957-014-0578-7

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