Initializing the variables

  The user must provide initial values for the variables. This may be done by calling the script init.m, which sets default values as follows, assuming that a scale factor is available in the workspace. The choice of is discussed further below.

,

structures, each with three fields:

,

the block diagonal matrix variables and , which must be positive definite. The default rule used by init.m is to set both to times the identity matrix.

,

the block vectors and , whose blocks must lie in the interior of their quadratic cones (see (2)). The default rule used by init.m is to set the first entry in each block to and the rest to zero.

,

the vectors and , which must be positive. The default rule used by init.m is to set all components to .

The dual variable y. Any initial values may be used; sets this to zero.

If the block diagonal matrices and have more than one block, they must be stored as sparse matrices. If they contain a single block, it is recommended that they be provided in full format, as the solutions will most likely be full. The vectors are normally stored using full format.

The proper choice of is highly problem dependent. The routine setopt.m sets to a default value of 100, but it may be necessary to change this to a larger value. On the other hand, often is satisfactory and results in a smaller number of iterations.