In this paper we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to $1$. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also not linear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that $0$ is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.
On the image regularity conditions
PAPPALARDO, MASSIMO
2004-01-01
Abstract
In this paper we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to $1$. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also not linear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that $0$ is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
