Journal of Convex Analysis 31 (2024), No. 4, 1151--1163
Copyright Heldermann Verlag 2024
On Second Order Sufficient Conditions for a Minimum
Alexander D. Ioffe
Department of Mathematics, Technion, Haifa, Israel
ioffe@technion.ac.il
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.
Keywords: Optimization problem, mathematical programming, local solution, tangent cone, critical cone.
MSC: 49K05.
[ Fulltext-pdf (130 KB)] for subscribers only.