Optimality conditions and duality results for a robust bi-level programming problem

Shivani Saini, Navdeep Kailey*, Izhar Ahmad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Robust bi-level programming problems are a newborn branch of optimization theory. In this study, we have considered a bi-level model with constraint-wise uncertainty at the upper-level, and the lower-level problem is fully convex. We use the optimal value reformulation to transform the given bi-level problem into a single-level mathematical problem and the concept of robust counterpart optimization to deal with uncertainty in the upper-level problem. Necessary optimality conditions are beneficial because any local minimum must satisfy these conditions. As a result, one can only look for local (or global) minima among points that hold the necessary optimality conditions. Here we have introduced an extended non-smooth robust constraint qualification (RCQ) and developed the KKT type necessary optimality conditions in terms of convexifactors and subdifferentials for the considered uncertain two-level problem. Further, we establish as an application the robust bi-level Mond-Weir dual (MWD) for the considered problem and produce the duality results. Moreover, an example is proposed to show the applicability of necessary optimality conditions.

Original languageEnglish
Pages (from-to)525-539
Number of pages15
JournalRAIRO - Operations Research
Issue number2
StatePublished - 1 Mar 2023

Bibliographical note

Publisher Copyright:
© 2023 The authors. Published by EDP Sciences, ROADEF, SMAI.


  • Constraint qualification
  • Mond-Weir dual
  • Optimality conditions
  • Robust counterpart
  • Uncertainty

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Management Science and Operations Research


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