This article concerns cautious classification models that are allowed to predict a set of class labels or reject make prediction when the uncertainty in is high. set-valued approach equivalent task acceptance region learning, which aims identify subsets input space, each guarantees cover observations with at least predetermined probability. We propose directly learn regions through risk minimiz...

In the nonparametric regression problem, one is given a set of vector valued variables 3 (termed carriers) and with each an associated scalar quantity Y (termed the response). This set of carriers and associated responses CYi,Xil (l<i<N) is termed the training sample. In addition (usually at some later time), one is given another set of vector valued variables {Ljl (lsj<M) without corresponding...

The article considers a particular class of optimization problems involving set-valued stochastic equilibrium constraints. A solution procedure is developed by relying on an approximation scheme for the equilibrium constraints, based on regularization, that replaces them by equilibrium constraints involving only single-valued Lipschitz continuous functions. In addition, sampling has the further...

In this paper, we consider different kinds of generalized invexity for vector valued functions and a vector optimization problem. Some relations between some vector variational-like inequalities and a vector optimization problem are established using the properties of Mordukhovich limiting subdifferentials under C − η−strong pseudomonotonicity. Mathematics Subject Classification (2010): 26A51, ...