2022/06/06 by Bauschke, Heinz H., Bendit, Theo, Wang, Hansen
#52A07 (Secondary) #90C25 (Primary) 46A55 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2206.02694
Let C be a closed convex subset of a real Hilbert space containing the origin, and assume that K is the homogenization cone of C, i.e., the smallest closed convex cone containing C × \1\. Homogenization cones play an important role in optimization as they include, for instance, the second-order/Lorentz/"ice cream" cone. In this note, we discuss the polar cone of K as well as an algorithm for finding the projection onto K provided that the projection onto C is available. Various examples illustrate our results.