Geodesic
No-Gap Second-Order Conditions under n-Polyhedric Constraints and Finitely Many Nonlinear Constraints
Journal of convex analysis, Tome 27 (2020) no. 2, pp. 733-751
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We consider an optimization problem subject to an abstract constraint and finitely many nonlinear constraints. Using the recently introduced concept of n-polyhedricity, we are able to provide second-order optimality conditions under weak regularity assumptions. In particular, we prove necessary optimality conditions of first and second order under the constraint qualification of Robinson, Zowe and Kurcyusz. Similarly, sufficient optimality conditions are stated. The gap between both conditions is as small as possible.
Classification : 49K27
Mots-clés : Second order optimality condition, critical cone, polyhedricity, Legendre form, non-unique multiplier 
@article{JCA_2020_27_2_JCA_2020_27_2_a15,
     author = {G. Wachsmuth},
     title = {No-Gap {Second-Order} {Conditions} under {n-Polyhedric} {Constraints} and {Finitely} {Many} {Nonlinear} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {733--751},
     year = {2020},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a15/}
}
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G. Wachsmuth. No-Gap Second-Order Conditions under n-Polyhedric Constraints and Finitely Many Nonlinear Constraints. Journal of convex analysis, Tome 27 (2020) no. 2, pp. 733-751. http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a15/