Some characterizations of robust optimal solutions for uncertain fractional optimization and applications

Xiang-Kai Sun; Xian-Jun Long; Hong-Yong Fu; Xiao-Bing Li

doi:10.3934/jimo.2016047

Article Contents

2017, Volume 13, Issue 2: 803-824. Doi: 10.3934/jimo.2016047

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Some characterizations of robust optimal solutions for uncertain fractional optimization and applications

1.
College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2.
School of Management, Southwest University of Political Science and Law, Chongqing 401120, China
3.
College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, China

* Corresponding author: Hong-Yong Fu
* Corresponding author: Hong-Yong Fu

Received: July 31, 2015

Revised: December 31, 2015

Published: August 2017

This research was supported by the National Natural Science Foundation of China (11301570,11471059,71501162), the Basic and Advanced Research Project of CQ CSTC (cstc2015jcyjA00002, cstc2015jcyjB00001, cstc2015jcyjBX0131), the Education Committee Project Research Foundation of Chongqing (KJ1500626), the Southwest University of Political Science and Law (2014XZQN-17), and the China Postdoctoral Science Foundation (2015M580770).

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Abstract

In this paper, following the framework of robust optimization, we consider robust optimal solutions for a fractional optimization problem in the face of data uncertainty both in the objective and constraints. To this end, by using the properties of the subdifferential sum formulae, we first introduce some robust basic subdifferential constraint qualifications, and then obtain some completely characterizations of the robust optimal solutions of this uncertain fractional optimization problem. We show that our results encompass as special cases some optimization problems considered in the recent literature. Moreover, as applications, the proposed approach is applied to investigate weakly robust efficient solutions for multi-objective fractional optimization problems in the face of data uncertainty both in the objective and constraints.

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Mathematics Subject Classification: Primary: 90C29, 90C32; Secondary: 90C46.

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