We propose a method to learn simultaneously a vector-valued function and a kernel between its components. The obtained kernel can be used both to improve learning performance and to reveal structures in the output space which may be important in their own right. Our method is based on the solution of a suitable regularization problem over a reproducing kernel Hilbert space of vector-valued func...

The exactness of the penalization for the exact l1 penalty function method used for solving nonsmooth constrained optimization problems with both inequality and equality constraints are presented. Thus, the equivalence between the sets of optimal solutions in the nonsmooth constrained optimization problem and its associated penalized optimization problem with the exact l1 penalty function is es...

This paper studies functionals defined by multiple integrals associated to differential forms on the jet bundle of first order corresponding to some Riemannian manifolds; the domain of these functionals consists in submanifold maps satisfying certain conditions of integrability. Our idea is to give geometric properties to the domain of a functional allowing us to properly define convexity. The ...

Abstract In this paper, for a nonsmooth semi-infinite multiobjective programming with locally Lipschitz data, some weak and strong Karush-KuhnTucker type optimality conditions are derived. The necessary conditions are proposed under a constraint qualification, and the sufficient conditions are explored under assumption of generalized invexity. All results are expressed in terms of Clarke subdif...

The symmetric function class interacts heavily with other types of functions. One these is the pre-invex class, which strongly related to symmetry theory. This paper proposes a novel fuzzy fractional extension Hermite-Hadamard, Hermite-Hadamard-Fejér, and Pachpatte type inequalities for up down fuzzy-number-valued mappings. Using operators, several generalizations have been developed, where wel...