Geodesic
A globally convergent non-interior point algorithm with full Newton step for second-order cone programming
Applications of Mathematics, Tome 54 (2009) no. 5, pp. 447-464.

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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.
DOI : 10.1007/s10492-009-0029-1
Classification : 65K05, 65Y20, 90C25, 90C30, 90C51
Keywords: non-interior point algorithm; second-order cone programming; Jordan product; optimality condition; central path 
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     title = {A globally convergent non-interior point algorithm with full {Newton} step for second-order cone programming},
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Fang, Liang; He, Guoping; Sun, Li. A globally convergent non-interior point algorithm with full Newton step for second-order cone programming. Applications of Mathematics, Tome 54 (2009) no. 5, pp. 447-464. doi : 10.1007/s10492-009-0029-1. http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0029-1/

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