A globally convergent non-interior point algorithm with full Newton step for second-order cone programming

Liang Fang; Guoping He; Li Sun

Applications of Mathematics (2009)

  • Volume: 54, Issue: 5, page 447-464
  • ISSN: 0862-7940

Abstract

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A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of A to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm.

How to cite

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Fang, Liang, He, Guoping, and Sun, Li. "A globally convergent non-interior point algorithm with full Newton step for second-order cone programming." Applications of Mathematics 54.5 (2009): 447-464. <http://eudml.org/doc/37832>.

@article{Fang2009,
abstract = {A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of $A$ to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm.},
author = {Fang, Liang, He, Guoping, Sun, Li},
journal = {Applications of Mathematics},
keywords = {non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path; non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path},
language = {eng},
number = {5},
pages = {447-464},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A globally convergent non-interior point algorithm with full Newton step for second-order cone programming},
url = {http://eudml.org/doc/37832},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Fang, Liang
AU - He, Guoping
AU - Sun, Li
TI - A globally convergent non-interior point algorithm with full Newton step for second-order cone programming
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 5
SP - 447
EP - 464
AB - A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of $A$ to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm.
LA - eng
KW - non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path; non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path
UR - http://eudml.org/doc/37832
ER -

References

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