| # Second-Order Cone Programming
| The second-order cone in is the set of vectors with . The picture shows part of the cone, and a slice (at ). For some strange reason, this set is called an ‘‘ice-cream cone’’. Second-order cone programming (SOCP) is a generalization of linear and quadratic programming that allows for affine combination of variables to be constrained inside second-order cones. The SOCP model includes as special cases problems with convex quadratic objective and constraints. SOCP models are particularly useful in geometry problems, as well as in linear programs where the data is imprecisely known. We explore this further here.
Outline Second-order cone inequalities Standard forms Group sparsity and the -norm trick Applications Exercises