Two-dimensional Second-Order Cone Programming

Yu Xia

International Journal of Operational Research, 2009, vol. 5, issue 4, 468-484

Abstract: 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.

Keywords: SOCP; second-order cone programming; linear programming; simplex method; pivoting; duality; linear transformations. (search for similar items in EconPapers)
Date: 2009
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