Geodesic
A new constraint qualification for optimality of nonconvex nonsmooth optimization problems
Filomat, Tome 36 (2022) no. 12, p. 4041

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In this paper, we study the nonconvex nonsmooth optimization problem (P) of minimizing a tangentially convex function with inequality constraints where the constraint functions are tangentially convex. This is done by using the cone of tangential subdifferentials together with a new constraint qualification. Indeed, we present a new constraint qualification to guarantee that Karush-Kuhn-Tucker conditions are necessary and sufficient for optimality of the problem (P). Moreover, various nonsmooth (generalized) constraint qualifications that are a modification of the well known constraint qualifications are investigated. Several illustrative examples are presented to clarify the connection between nonsmooth constraint qualifications and new constraint qualification.
DOI : 10.2298/FIL2212041B
Classification : 90C26, 90C30, 90C46
Keywords: nonconvex optimization, nonsmooth optimization, tangentially convex function, tangentially constraint qualification, nonsmooth constraint qualification, nonconvex constraint, optimality condition, Karush-Kuhn-Tucker condition, tangential subdifferential 
Fatemeh Bazargan; Hossein Mohebi. A new constraint qualification for optimality of nonconvex nonsmooth optimization problems. Filomat, Tome 36 (2022) no. 12, p. 4041 . doi: 10.2298/FIL2212041B
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     title = {A new constraint qualification for optimality of nonconvex nonsmooth optimization problems},
     journal = {Filomat},
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     year = {2022},
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     doi = {10.2298/FIL2212041B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212041B/}
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