We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.
"Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem." J. Appl. Math. 2012 1 - 7, 2012. https://doi.org/10.1155/2012/617485