Our algorithms can start with an infeasible starting point. However, the performance of these algorithms is quite sensitive to the choice of the initial iterate. As observed in , it is desirable to choose an initial iterate that at least has the same order of magnitude as an optimal solution of the SDP. Suppose the matrices and C are block-diagonal of the same structure, each consisting of L blocks of square matrices of dimensions . Let and denote the ith block of and C, respectively. If a feasible starting point is not known, we recommend that the following initial iterate be used:
where , is the identity matrix of order , and
By multiplying the identity matrix by the factors and for each i, the initial iterate has a better chance of having the same order of magnitude as an optimal solution of the SDP.
The initial iterate
above is set by calling infeaspt.m, with initial line
function [X0,y0,Z0] = infeaspt(blk,A,C,b,options),
where options = 1 (default) corresponds to the
initial iterate just described; and options = 2 corresponds
to the choice where X0, Z0 are identity matrices
and y0 is a zero vector.