Regularity conditions and Farkas-type results for systems with fractional functions
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 5, pp. 1369-1384.

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results.

DOI : 10.1051/ro/2019070
Classification : 90C26, 90C32, 90C46
Mots-clés : Regularity conditions, Farkas-type results, fractional functions 
@article{RO_2020__54_5_1369_0,
     author = {Sun, Xiangkai and Long, Xian-Jun and Tang, Liping},
     title = {Regularity conditions and {Farkas-type} results for systems with fractional functions},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1369--1384},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {5},
     year = {2020},
     doi = {10.1051/ro/2019070},
     mrnumber = {4127958},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019070/}
}
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Sun, Xiangkai; Long, Xian-Jun; Tang, Liping. Regularity conditions and Farkas-type results for systems with fractional functions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 5, pp. 1369-1384. doi : 10.1051/ro/2019070. http://www.numdam.org/articles/10.1051/ro/2019070/

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