A Study on handling dense columns in interior point methods for linear programming (An efficient implementation of Schur complement method)

내부점 방법에서 밀집열 처리에 관한 연구 (Schur 상보법의 효율적인 구현)

The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization to solve AΘA$^{T}$ $\Delta$y=b. If the coefficient matrix A has dense columns then the matrix AΘA$^{T}$ becomes a dense matrix. This causes Cholesky factorization to be slow. The Schur complement method is applied to treat dense columns in many implementations but suffers from its numerical unstability. We study efficient implementation of Schur complement method. We achieve improvements in computational speed and numerical stability.rical stability.