Exploring the relationship among multiple sets of data from one same group
enables practitioners to make better decisions in medical science and
engineering. In this paper, we propose a sparse collaborative learning (SCL)
model, an optimization with double-sparsity constraints, to process the problem
with two sets of data and a shared response variable. It is capable of dealing
with the classification problems or the regression problems dependent on the
discreteness of the response variable as well as exploring the relationship
between two datasets simultaneously. To solve SCL, we first present some
necessary and sufficient optimality conditions and then design a gradient
projection Newton algorithm which has proven to converge to a unique locally
optimal solution globally with at least a quadratic convergence rate. Finally,
the reported numerical experiments illustrate the efficiency of the proposed
method.