Applications of Second Order Cone Programming

A significant special case of the problems which could be solved were those whose constraints were given by semidefinite cones. A Semidefinite Program (SDP) is an optimisation over the intersection of an affine set and cone of positive semidefinite matrices (Alizadeh and Goldfarb, 2001). Cone programming is discussed more in Section 3. Within semidefinite programming there is a smaller set of problems which can be modelled as Second Order Cone Programs (SOCPs), discussed more in Section 4. These have a wide range of applications, some of which are discussed in Section 5, and can still be solved efficiently using interior point methods. Lobo et al. (1998) justifies that the study of SOCPs in their own right is warranted. Software for solving SOCPs is now readily available, see Mittelmann (2012) for an overview on existing code.