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