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Initial iterates

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 [5], 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 tex2html_wrap_inline2161 and C are block-diagonal of the same structure, each consisting of L blocks of square matrices of dimensions tex2html_wrap_inline2757 . Let tex2html_wrap_inline2759 and tex2html_wrap_inline2761 denote the ith block of tex2html_wrap_inline2161 and C, respectively. If a feasible starting point is not known, we recommend that the following initial iterate be used:


where tex2html_wrap_inline2769 , tex2html_wrap_inline2771 is the identity matrix of order tex2html_wrap_inline2773 , and


By multiplying the identity matrix tex2html_wrap_inline2771 by the factors tex2html_wrap_inline2777 and tex2html_wrap_inline2779 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.