Solving Rank-Constrained Semidefinite Programs in Exact Arithmetic
Solving Rank-Constrained Semidefinite Programs in Exact Arithmetic
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active, this is a non-convex optimization problem, otherwise it is a semidefinite program. Both …