Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.
Bibliographical noteFunding Information:
Acknowledgements. The first author thanks the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for the support under the Small/Basic Research grant No. SB191005. The authors wish to thank the referees for their valuable suggestions which have considerably improved the presentation of the paper.
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021.
- Generalized convexity
- Robust duality
- Robust nonsmooth optimization
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science Applications
- Management Science and Operations Research