A Non-interior Point Continuation Algorithm Based on Orthogonal Projection for Second-Order Cone Programming

Based on orthogonal projection, a non-interior point continuation algorithm for second-order cone programming problems is proposed and analyzed. The main idea of the method is that we reformulate the complementary condition in the optimality conditions as a projection equation. Using this reformulation, we only need to solve a system of linear equations, compute two simple projections and perform one line search at each iteration. The algorithm can start from an arbitrary initial point, and doesn´t need that A has full row rank. The method is globally convergent under mild conditions. Preliminary numerical results demonstrate the effectiveness of the algorithm.