Geodesic
On Second Order Sufficient Conditions for a Minimum
Journal of convex analysis, Tome 31 (2024) no. 4, pp. 1151-1163
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The paper offers second order necessary and sufficient conditions for a sufficiently general class of optimization problems in Banach spaces. The reader can easily see that this is a ``no gap'' pair of conditions, although sufficient conditions (as usual) hold under some additional assumptions, mainly aimed to guarantee that tangent sets to the non-functional constraint set approximate the latter sufficiently well. In the last section we apply the results to a mathematical programming problem that contains, along with functional equality and inequality constraints, also a non-functional set constraint.
Classification : 49K05
Mots-clés : Optimization problem, mathematical programming, local solution, tangent cone, critical cone 
@article{JCA_2024_31_4_JCA_2024_31_4_a5,
     author = {A. D. Ioffe},
     title = {On {Second} {Order} {Sufficient} {Conditions} for a {Minimum}},
     journal = {Journal of convex analysis},
     pages = {1151--1163},
     year = {2024},
     volume = {31},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_4_JCA_2024_31_4_a5/}
}
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A. D. Ioffe. On Second Order Sufficient Conditions for a Minimum. Journal of convex analysis, Tome 31 (2024) no. 4, pp. 1151-1163. http://geodesic.mathdoc.fr/item/JCA_2024_31_4_JCA_2024_31_4_a5/