On approximate solutions and saddle point theorems for robust convex optimization

  • Xiang-Kai SunEmail author
  • Kok Lay Teo
  • Jing Zeng
  • Xiao-Le Guo
Original Paper


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.


Approximate optimal solutions Robust convex optimization Saddle point theorems 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina
  2. 2.School of Electrical Engineering, Computing and Mathematical SciencesCurtin UniversityPerthAustralia
  3. 3.Coordinated Innovation Center for Computable Modeling in Management ScienceTianjin University of Finance and EconomicsTianjinChina

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