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On approximate solutions and saddle point theorems for robust convex optimization

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Abstract

This paper provides some new results on robust approximate optimal solutions for convex optimization problems with data uncertainty. By using robust optimization approach (worst-case approach), we first establish necessary and sufficient optimality conditions for robust approximate optimal solutions of this uncertain convex optimization problem. Then, we introduce a Wolfe-type robust approximate dual problem and investigate robust approximate duality relations between them. Moreover, we obtain some robust approximate saddle point theorems for this uncertain convex optimization problem. We also show that our results encompass as special cases some optimization problems considered in the recent literature.

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Acknowledgements

The authors express their gratitude to the anonymous referees for their valuable comments and suggestions, which help to improve the paper. This research was supported by the Basic and Advanced Research Project of Chongqing (cstc2017jcyjBX0032, cstc2019jcyj-msxmX0605, cstc2015jcyjA00038), the ARC Discovery Grant (DP190103361), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201800837, KJ130705), the National Natural Science Foundation of China (11701057) and the Program for University Innovation Team of Chongqing (CXTDX201601026).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xiang-Kai Sun, Jing Zeng & Xiao-Le Guo

  2. School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA, 6845, Australia

    Kok Lay Teo

  3. Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Kok Lay Teo

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  1. Xiang-Kai Sun
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  2. Kok Lay Teo
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  3. Jing Zeng
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  4. Xiao-Le Guo
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Correspondence to Xiang-Kai Sun.

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Sun, XK., Teo, K.L., Zeng, J. et al. On approximate solutions and saddle point theorems for robust convex optimization. Optim Lett 14, 1711–1730 (2020). https://doi.org/10.1007/s11590-019-01464-3

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