Two-dimensional second-order cone programming

We show that the primal and dual 2-dimensional second-order cone programs in standard form are equivalent to the standard-form primal and dual linear programs via a linear transformation. We show how variables in the Second-Order Cone (SOC) programs and the linear programs are related by the transformation. Based on the transformation, we interpret the simplex method for two-dimensional Second-Order Cone Programming (SOCP). We show how pivot steps change the states of variables among interior, boundary, and zero. Finally, we give some applications of two-dimensional SOCP.