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SemidefiniteProgramming :: refine(SDP,Sequence)

refine(SDP,Sequence) -- refine an SDP solution

Synopsis

Description

This function uses Newton's method to improve the precision of an optimal primal/dual pair. The refined solution has relative error bounded by min(ErrorTolerance,2(-Bits)). The number of iterations made is at most Iterations.

i1 : P = sdp(matrix{{1,0},{0,2}}, matrix{{0,1},{1,0}}, matrix{{-1}});
i2 : (X0,y0) = (matrix{{.71, -.5}, {-.5, .35}}, matrix{{-1.41}})

o2 = (| .71 -.5 |, | -1.41 |)
      | -.5 .35 |

o2 : Sequence
i3 : (X1,y1) = refine(P,(X0,y0))

o3 = (| .707107 -.5     |, | -1.41421 |)
      | -.5     .353553 |

o3 : Sequence

      

See also