 Semidefinite programming

A semidefinite program optimizes a linear function subject to equalities between affine functions and positive semidefinite matrix inequalities. It generalizes linear programming: a diagonal matrix is a positive semidefinite matrix exactly when its diagonal entries are nonnegative. Matrix trace expresses the objective as $⟨C,X⟩=\mathrm{tr}(CX)$ for real symmetric matrices.

Semidefinite programming (SDP) is a subfield of convex optimization that deals with the minimization of a linear objective function subject to semidefinite constraints.