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A globally convergent non-interior point algorithm with full Newton step for second-order cone programming. (English) Zbl 1212.90299
Summary: 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 $$A$$ 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.

##### MSC:
 90C25 Convex programming 90C30 Nonlinear programming 90C51 Interior-point methods 65K05 Numerical mathematical programming methods 65Y20 Complexity and performance of numerical algorithms
SDPT3
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