The unique feature of the face algorithm \cite{pan14} is that it moves from face to face, rather than from vertex to vertex as the simplex algorithm. It uses the orthogonal projection of the negative objective gradient on the related null space as its search direction. Nevertheless, the algorithm is based on QR factorization, which would not be very amenable for large sparse problems. In this paper, we present a face algorithm using LU factorization instead. It not only retains the main advantages of the original face algorithm, but also adds some nice features.
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School of Mathematics, Southeast University, Nanjing 210096, China.
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