Two-dimensional second-order cone programming (Q840619)

Summary: We show that primal and dual 2-dimensional second-order cone programs in standard form are equivalent to standard-form primal and dual linear programs via a linear transformation. We show how variables in second-order cone (SOC) programs and linear programs are related by a transformation, based on which 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.