Open Access
Issue |
RAIRO-Oper. Res.
Volume 57, Number 2, March-April 2023
|
|
---|---|---|
Page(s) | 525 - 539 | |
DOI | https://doi.org/10.1051/ro/2023026 | |
Published online | 24 March 2023 |
- J.M. Abadie, On the Kuhn-Tucker theorem. Operations Research Center University of Calif Berkeley (1967). [Google Scholar]
- A. Aboussoror and S. Adly, A Fenchel-Lagrange duality approach for a bilevel programming problem with extremal-value function. J. Optim. Theory Appl. 149 (2011) 254–268. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Beck and M. Schmidt, A robust approach for modeling limited observability in bilevel optimization. Oper. Res. Lett. 49 (2021) 752–758. [CrossRef] [MathSciNet] [Google Scholar]
- A. Ben-Tal and A. Nemirovski, Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88 (2000) 411–424. [Google Scholar]
- J. Bracken and J.T. McGill, Mathematical programs with optimization problems in the constraints. Oper. Res. 21 (1973) 37–44. [CrossRef] [Google Scholar]
- C. Buchheim, D. Henke and F. Hommelsheim, On the complexity of robust bilevel optimization with uncertain follower’s objective. Preprint arXiv:2105.08378 (2021). [Google Scholar]
- Y. Chen and M. Florian, The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Optimization 32 (1995) 193–209. [CrossRef] [MathSciNet] [Google Scholar]
- J. Chen, E. Köbis and J.C. Yao, Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J. Optim. Theory Appl. 181 (2019) 411–436. [CrossRef] [MathSciNet] [Google Scholar]
- T.D. Chuong and V. Jeyakumar, Generalized farkas lemma with adjustable variables and two-stage robust linear programs. J. Optim. Theory Appl. 187 (2020) 488–519. [CrossRef] [MathSciNet] [Google Scholar]
- F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). [Google Scholar]
- S. Dempe and A.B. Zemkoho, On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem. Nonlinear Anal. Theory Methods Appl. 75 (2012) 1202–1218. [CrossRef] [Google Scholar]
- S. Dempe and A.B. Zemkoho, KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization. SIAM J. Optim. 24 (2014) 1639–1669. [CrossRef] [MathSciNet] [Google Scholar]
- S. Dempe and A.B. Zemkoho, Bilevel Optimization. Springer Cham (2020). [CrossRef] [Google Scholar]
- S. Dempe, J. Dutta and S. Lohse, Optimality conditions for bilevel programming problems. Optimization 55 (2006) 505–524. [CrossRef] [MathSciNet] [Google Scholar]
- S. Dempe, J. Dutta and B. Mordukhovich, New necessary optimality conditions in optimistic bilevel programming. Optimization 56 (2007) 577–604. [CrossRef] [MathSciNet] [Google Scholar]
- S. Dempe, N.A. Gadhi and M. El Idrissi, Optimality conditions in terms of convexificators for a bilevel multiobjective optimization problem. Optimization 69 (2020) 1811–1830. [CrossRef] [MathSciNet] [Google Scholar]
- J. Dutta and S. Chandra, Convexifactors, generalized convexity, and optimality conditions. J. Optim. Theory Appl. 113 (2002) 41–64. [CrossRef] [MathSciNet] [Google Scholar]
- N.A. Gadhi, K. Hamdaoui and M. El idrissi, Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a ψ reformulation. Optimization 69 (2020) 681–702. [CrossRef] [MathSciNet] [Google Scholar]
- N.A. Gadhi, Comments on a note on the paper optimality conditions for optimistic bilevel programming problem using convexifactors. J. Optim. Theory Appl. 189 (2021) 938–943. [CrossRef] [MathSciNet] [Google Scholar]
- M. Goerigk, K. Adam and Z. Pawel, Robust two-stage combinatorial optimization problems under convex uncertainty. Preprint arXiv:1905.02469 (2019). [Google Scholar]
- J.B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis, Springer Science & Business Media (2004). [Google Scholar]
- M. Jennane, E.M. El Kalmoun and L. El Fadil, Optimality conditions for nonsmooth multiobjective bilevel optimization using tangential subdifferentials. RAIRO: OR 55 (2021) 3041–3048. [CrossRef] [EDP Sciences] [Google Scholar]
- V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Optim. Theory Appl. 101 (1999) 599–621. [CrossRef] [MathSciNet] [Google Scholar]
- K.O. Kenneth, G. Yu and Q. Zhang, Strong duality for standard convex programs. Math. Methods Oper. Res. 94 (2018) 413–436. [Google Scholar]
- P. Kesarwani, P.K. Shukla, J. Dutta and K. Deb, Approximations for pareto and proper pareto solutions and their KKT conditions. Math. Methods Oper. Res. 96 (2022) 123–148. [CrossRef] [MathSciNet] [Google Scholar]
- B. Kohli, Optimality conditions for optimistic bilevel programming problem using convexifactors. J. Optim. Theory Appl. 152 (2012) 632–651. [Google Scholar]
- L. Lafhim, N. Gadhi, K. Hamdaoui and F. Rahou, Necessary optimality conditions for a bilevel multiobjective programming problem via a ψ-reformulation. Optimization 67 (2018) 2179–2189. [CrossRef] [MathSciNet] [Google Scholar]
- G.M. Lee and P.T. Son, On nonsmooth optimality theorems for robust optimization problems. Bull. Korean Math. Soc. 51 (2014) 287–301. [CrossRef] [MathSciNet] [Google Scholar]
- R. Lotfi, N. Mardani and G.M. Weber, Robust bi-level programming for renewable energy location. Int. J. Energy Res. 45 (2021) 7521–7534. [CrossRef] [Google Scholar]
- B.S. Mordukhovich, Variational Analysis and Generalized Differentiation I: Basic Theory, Springer Science & Business Media (2006). [Google Scholar]
- B.S. Mordukhovich, N.M. Nam and N.D. Yen, Subgradients of marginal functions in parametric mathematical programming. Math. Program. 116 (2009) 369–396. [CrossRef] [MathSciNet] [Google Scholar]
- A.S. Safaei, S. Farsad and M.M. Paydar, Robust bi-level optimization of relief logistics operations. Appl. Math. Model 56 (2018) 359–380. [CrossRef] [MathSciNet] [Google Scholar]
- S.K. Suneja and B. Kohli, Optimality and duality results for bilevel programming problem using convexifactors. J. Optim. Theory Appl. 150 (2011) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
- P. Swain and A.K. Ojha, Bi-level optimization approach for robust mean-variance problems. RAIRO:OR 55 (2021) 2941–2961. [CrossRef] [EDP Sciences] [Google Scholar]
- T. Van Su, D.D. Hang and N.C. Dieu, Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints. Comput. Appl. Math. 40 (2021) 1–26. [CrossRef] [Google Scholar]
- H. Von Stackelberg, Marktform und Gleichgewicht. Springer (1934). [Google Scholar]
- H. Von Stackelberg, Marktform and Gleichgewicht, Springer-verlag berlin (1934) [Engl. Transl.: The Theory of the Market Economy (1954)]. [Google Scholar]
- J. Xiong, S. Wang and T.S. Ng, Robust bilevel resource recovery planning. Prod. Oper. Manag. 30 (2021) 2962–2992. [CrossRef] [Google Scholar]
- A. Yezza, First-order necessary optimality conditions for general bilevel programming problems. J. Optim. Theory Appl. 89 (1996) 189–219. [CrossRef] [MathSciNet] [Google Scholar]
- A.B. Zemkoho and S. Zhou, Theoretical and numerical comparison of the Karush–Kuhn–Tucker and value function reformulations in bilevel optimization. Comput. Optim. Appl. 78 (2021) 625–674. [CrossRef] [MathSciNet] [Google Scholar]
- B. Zeng, H. Dong, R. Sioshansi, F. Xu and M. Zeng, Bilevel robust optimization of electric vehicle charging stations with distributed energy resources. IEEE Trans. Ind. Appl. 56 (2020) 5836–5847. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.