A sparse MPC solver for walking motion generation (old version).: Notes on implementation

A sparse MPC solver for walking motion generation (old version).

Cholesky decomposition

The Cholesky factor of the Schur complement must be formed on each iteration. Due to the differences in the Schur complement (see 'Schur complement (IP method)') caused by addition of the logarithic barrier, the Cholesky factor is not so well structured as in the case of the active set method.

Each 6x6 $\mbm{L}_{ij}$ matrix of the factor (see 'Cholesky decomposition of Schur complement') must be stored. The matrices are stored sequentially from the top left to the bottom right.