Preprint A190/2002
On Optimality Conditions for Cone-Constrained Optimization

M.V. Solodov | Izmailov, A.F.

**Keywords: **
optimality conditions | cone constraints | regularity

We consider feasible sets given by conic constraints, where
the cone defining the constraints is convex with nonempty interior.
We study the case where the feasible set is
not assumed to be regular in the classical sense of Robinson
and obtain a constructive description of the tangent cone
under a certain new second-order regularity condition.
This condition contains classical regularity as a special case,
while being weaker when constraints are twice differentiable.
Assuming that the cone defining the constraints is finitely
generated, we also derive a special form of
primal-dual optimality conditions for the corresponding
constrained optimization problem. Our results subsume optimality
conditions for both the classical regular and second-order
regular cases, while still being meaningful
in the more general setting in the sense
that the multiplier associated with the objective function is
nonzero.