Correction to: Positivity (2020) 24:1399–1417 https://doi.org/10.1007/s11117-020-00737-x
Dutta et al. [3] have recently published a correction of the well-known result of Dutta and Chandra [2, Theorem 3.5]. Using a counterexample, they proved that Dutta and Chandra’s result is not correct and then provided a true statement of it (see [3, Theorem 2.1]) under the assumption that the contingent cone to the feasible set at the considered point is convex.
As the conclusion of [2, Theorem 3.5] was used in the proof of [1, Theorem 10], specifically for transitioning from
to
we have to correct our results by adding the missing convexity of the contingent cone \(T\left( E,\overline{x}\right) \) to the statement of [1, Theorem 10] and the subsequent outcomes. This additional condition is crucial for the validity of our results.
References
Dempe, S., Gadhi, N., Lafhim, L.: Optimality conditions for pessimistic bilevel problems using convexificator. Positivity 24, 1399–1417 (2020)
Dutta, J., Chandra, S.: Convexifactors, generalized convexity, and optimality conditions. J. Optim. Theory Appl. 113, 41–64 (2002)
Dutta, J., Chandra, J., Rimpi, S., Lalitha, C.S.: Correction to: Convexifactors, generalized convexity, and optimality condition. J. Optim. Theory Appl. (2023). https://doi.org/10.1007/s10957-023-02190-8
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Dempe, S., Gadhi, N. & Lafhim, L. Correction to: Optimality conditions for pessimistic bilevel problems using convexificator. Positivity 28, 6 (2024). https://doi.org/10.1007/s11117-023-01009-0
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DOI: https://doi.org/10.1007/s11117-023-01009-0