Optimization Seminar: Dr. Roman Sznajder

Title: Orthogonal projections and positive operators on the extended second order cone (continued from last week)

The so-called Extended Second Order Cone (ESOC) is quite an elusive object and appears as a generalization of the second order (Lorentz) cone. We will provide explicit formulas for orthogonal (metric) projections onto ESOC and its dual. We will also attempt to characterize positive operators on this cone (rather on its dual). A full characterization is yet unknown.  The results presented are based on the work of S.Z. Nemeth and G. Zhang, O.P. Ferreira and S.Z. Nemeth, and, partially, R. Sznajder.