Title: Two-dimensional Second-Order Cone Programming

Authors: Yu Xia

Addresses: School of Mathematics, University of Birmingham, Edgbaston, Birmingham, UK

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.

DOI: 10.1504/IJOR.2009.025704

International Journal of Operational Research, 2009 Vol.5 No.4, pp.468 - 484

Available online: 23 May 2009 *

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