doi: 10.3934/jimo.2021103

A note on the paper "Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem"

LAMA, FSDM, Sidi Mohamed Ben Abdellah University, Fez, Morocco

* Corresponding author: Nazih Abderrazzak Gadhi

Received  November 2020 Revised  March 2021 Published  May 2021

In this work, some reasoning's mistakes in the paper by Kohli (doi:10.3934/jimo.2020114) are highlighted. Furthermore, we correct the flaws, propose a correct formulation of the main result (Theorem 5.1) and give alternative proofs.

Citation: Nazih Abderrazzak Gadhi. A note on the paper "Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem". Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021103
References:
[1]

C. R. Bector, S. Chandra and J. Dutta, Principles of Optimization Theory, Narosa Publishing House, 2005. Google Scholar

[2]

F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.  Google Scholar

[3]

S. DempeJ. Dutta and B. S. Mordukhovich, New necessary optimality conditions in optimistic bilevel programming, Optimization, 56 (2007), 577-604.  doi: 10.1080/02331930701617551.  Google Scholar

[4]

S. DempeN. Gadhi and A. B. Zemkoho, New optimality conditions for the semivectorial bilevel optimization problem, Journal of Optimization Theory and Applications, 157 (2013), 54-74.  doi: 10.1007/s10957-012-0161-z.  Google Scholar

[5]

S. Dempe and P. Mehlitz, Semovectorial bilevel programming versus scalar bilevel programming, Optimization, 69 (2020), 657-679.  doi: 10.1080/02331934.2019.1625900.  Google Scholar

[6]

J. Dutta and S. Chandra, Convexifactors, generalized convexity, and optimality conditions, Journal of Optimization Theory and Applications, 113 (2002), 41-64.  doi: 10.1023/A:1014853129484.  Google Scholar

[7]

N. GadhiK. Hamdaoui and M. El Idrissi, Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a $\Psi $ reformulation, Optimization, 69 (2020), 681-702.  doi: 10.1080/02331934.2019.1625901.  Google Scholar

[8]

N. Gadhi, K. Hamdaoui and M. El Idrissi, Optimality conditions for a multiobjective bilevel optimization problem involving set valued constraints, Optimization, (2020). doi: 10.1080/02331934.2020.1768253.  Google Scholar

[9]

B. Kohli, Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem, Journal of Industrial and Management Optimization, (2020). doi: 10.3934/jimo.2020114.  Google Scholar

[10]

D. V. Luu, Optimality condition for local efficient solutions of vector equilibrium problems via convexificators and applications, Journal of Optimization Theory and Applications, 171 (2016), 643-665.  doi: 10.1007/s10957-015-0815-8.  Google Scholar

[11]

K. Shimizu, Y. Ishizuka and J. F. Bard, Nondifferentiable and two-level mathematical programming, Dordrecht, Kluwer Academic Publishers, 1997. doi: 10.1007/978-1-4615-6305-1.  Google Scholar

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T. Tanino and T. Ogawa, An algorithm for solving two-level convex optimization problems, International Journal of Systems Science, 15 (1984), 163-174.  doi: 10.1080/00207728408926552.  Google Scholar

show all references

References:
[1]

C. R. Bector, S. Chandra and J. Dutta, Principles of Optimization Theory, Narosa Publishing House, 2005. Google Scholar

[2]

F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.  Google Scholar

[3]

S. DempeJ. Dutta and B. S. Mordukhovich, New necessary optimality conditions in optimistic bilevel programming, Optimization, 56 (2007), 577-604.  doi: 10.1080/02331930701617551.  Google Scholar

[4]

S. DempeN. Gadhi and A. B. Zemkoho, New optimality conditions for the semivectorial bilevel optimization problem, Journal of Optimization Theory and Applications, 157 (2013), 54-74.  doi: 10.1007/s10957-012-0161-z.  Google Scholar

[5]

S. Dempe and P. Mehlitz, Semovectorial bilevel programming versus scalar bilevel programming, Optimization, 69 (2020), 657-679.  doi: 10.1080/02331934.2019.1625900.  Google Scholar

[6]

J. Dutta and S. Chandra, Convexifactors, generalized convexity, and optimality conditions, Journal of Optimization Theory and Applications, 113 (2002), 41-64.  doi: 10.1023/A:1014853129484.  Google Scholar

[7]

N. GadhiK. Hamdaoui and M. El Idrissi, Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a $\Psi $ reformulation, Optimization, 69 (2020), 681-702.  doi: 10.1080/02331934.2019.1625901.  Google Scholar

[8]

N. Gadhi, K. Hamdaoui and M. El Idrissi, Optimality conditions for a multiobjective bilevel optimization problem involving set valued constraints, Optimization, (2020). doi: 10.1080/02331934.2020.1768253.  Google Scholar

[9]

B. Kohli, Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem, Journal of Industrial and Management Optimization, (2020). doi: 10.3934/jimo.2020114.  Google Scholar

[10]

D. V. Luu, Optimality condition for local efficient solutions of vector equilibrium problems via convexificators and applications, Journal of Optimization Theory and Applications, 171 (2016), 643-665.  doi: 10.1007/s10957-015-0815-8.  Google Scholar

[11]

K. Shimizu, Y. Ishizuka and J. F. Bard, Nondifferentiable and two-level mathematical programming, Dordrecht, Kluwer Academic Publishers, 1997. doi: 10.1007/978-1-4615-6305-1.  Google Scholar

[12]

T. Tanino and T. Ogawa, An algorithm for solving two-level convex optimization problems, International Journal of Systems Science, 15 (1984), 163-174.  doi: 10.1080/00207728408926552.  Google Scholar

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