recoverSolution -- factor a rank one positive semidefinite matrix

Synopsis

Usage:

sol = recoverSolution(mon,X)

sol = recoverSolution(sdpsol)
Inputs:
- mon, a matrix, of monomials
- X, a matrix, the moment matrix
- sdpsol, an instance of the type SDPResult,
Outputs:
- sol, a list, the optimal solution

Description

This method attempts to find the optimizing solutions of a sum-of-squares problem by checking if the moment matrix is rank one. In this case it factorizes the matrix and returns the defining vector.

i1 : R = RR[x,y];

i2 : mon = matrix {{1},{x},{y}};

             3      1
o2 : Matrix R  <-- R

i3 : X = matrix(RR, {{1,0,1},{0,0,0},{1,0,1}} );

                3         3
o3 : Matrix RR    <-- RR
              53        53

i4 : sol = recoverSolution(mon,X)

o4 = {x => 0, y => 1}

o4 : List

See lowerBound for how to use it to find a point realizing a lower bound.

Ways to use recoverSolution :

recoverSolution(Matrix,Matrix)
recoverSolution(SDPResult)

For the programmer

The object recoverSolution is a method function.

recoverSolution -- factor a rank one positive semidefinite matrix

Synopsis

Description

See also

Ways to use recoverSolution :

For the programmer