Second Order Cone Programming (SOCP)

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There is one exception to the PSD requirement; that is, there is an additional form of quadratic constraint which is accepted but is not covered by the general formulation in Identifying a Quadratically Constrained Program (QCP). Technically, the quadratically constrained problem class that the barrier optimizer solves is a Second-Order Cone Program (SOCP). ILOG CPLEX, through its preprocessing feature, makes the translation to SOCP for you, transparently, returning the solution in terms of your original formulation. A constraint will be accepted for solution by the barrier optimizer if it can be transformed to the following convex second-order cone constraint: