Standard Forms of SOCP
Second-order coneThe second-order cone in ![]() This set is convex, since it is the intersection of (an infinite number of) half-spaces: ![]() It is a cone, since it is invariant by scaling: if
Example: Magnitude constraints on affine complex vectors. Rotated second-order coneThe rotated second-order cone in ![]() Note that the rotated second-order cone in ![]() This is, Rotated second-order cone constraints are useful to describe quadratic convex inequalities. Precisely, if ![]() is equivalent to the existence of ![]() where Second-order cone inequalitiesA second-order cone (SOC) inequality on a vector This is a constraint of the form ![]() where Examples: |