In this paper is firstly pointed out the strict relationship existing between the optimality of a point x0, belonging to a feasible region S, and the behaviour of the objective function along the directions of the cone of tangents to S at x0. Such a relationship is established either for a directionally differentiable and locally lipschitz continuous function at x0 or for a differentiable function at x0 and allows finding first and second order optimality conditions in the case where xo is the vertex of a star shaped set S or, as a special case, is the vertex of a polyhedral cone. Finally, relationships between optimality at the vertex x0 of a star shaped set S and optimailty at x0 along the directions of S are investigated by means of generalized concavity.
Alcune condizioni di ottimalità relative ad un insieme stellato
CAMBINI, RICCARDO
1993
Abstract
In this paper is firstly pointed out the strict relationship existing between the optimality of a point x0, belonging to a feasible region S, and the behaviour of the objective function along the directions of the cone of tangents to S at x0. Such a relationship is established either for a directionally differentiable and locally lipschitz continuous function at x0 or for a differentiable function at x0 and allows finding first and second order optimality conditions in the case where xo is the vertex of a star shaped set S or, as a special case, is the vertex of a polyhedral cone. Finally, relationships between optimality at the vertex x0 of a star shaped set S and optimailty at x0 along the directions of S are investigated by means of generalized concavity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
