article · International Journal of Operational Research · 2009

Two-dimensional Second-Order Cone Programming

Cited by 1Abstract and details only

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.

Cite this paper

APA 7

Xia, Y. (2009). Two-dimensional Second-Order Cone Programming. International Journal of Operational Research, 5(4), 468. https://doi.org/10.1504/ijor.2009.025704

MLA 9

Xia, Yu. “Two-dimensional Second-Order Cone Programming.” International Journal of Operational Research, vol. 5, no. 4, 2009, p. 468, https://doi.org/10.1504/ijor.2009.025704.

Chicago

Xia, Yu. 2009. “Two-dimensional Second-Order Cone Programming.” International Journal of Operational Research 5 (4): 468. https://doi.org/10.1504/ijor.2009.025704.

Harvard

Xia, Y. (2009) ‘Two-dimensional Second-Order Cone Programming’, International Journal of Operational Research, 5(4), p. 468. Available at: https://doi.org/10.1504/ijor.2009.025704.

BibTeX

@article{xia2009dimensional,
  title = {{Two-dimensional Second-Order Cone Programming}},
  author = {Xia, Yu},
  journal = {International Journal of Operational Research},
  volume = {5},
  number = {4},
  pages = {468},
  year = {2009},
  doi = {10.1504/ijor.2009.025704}
}

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