Direct Quadratic Programs¶

\[\begin{split}\min_x & \{\; \frac{1}{2} x^T Q x + c^T x \; | \; A x = b \;\wedge\; x \ge 0 \;\}, \\ \max_{y,z} & \{\; -\frac{1}{2} r^T Q^\dagger r - b^T y \; | \; r = A^T y - z + c \in \text{range}(Q) \;\wedge\; z \ge 0 \;\}\end{split}\]

Python API¶

QPDirect(Q, A, b, c, x, y, z[, ctrl=None])¶

C++ API¶

void QP(const Matrix<Real> &Q, const Matrix<Real> &A, const Matrix<Real> &b, const Matrix<Real> &c, Matrix<Real> &x, Matrix<Real> &y, Matrix<Real> &z, const qp::direct::Ctrl<Real> &ctrl = qp::direct::Ctrl<Real>())¶

void QP(const ElementalMatrix<Real> &Q, const ElementalMatrix<Real> &A, const ElementalMatrix<Real> &b, const ElementalMatrix<Real> &c, ElementalMatrix<Real> &x, ElementalMatrix<Real> &y, ElementalMatrix<Real> &z, const qp::direct::Ctrl<Real> &ctrl = qp::direct::Ctrl<Real>())¶

void QP(const SparseMatrix<Real> &Q, const SparseMatrix<Real> &A, const Matrix<Real> &b, const Matrix<Real> &c, Matrix<Real> &x, Matrix<Real> &y, Matrix<Real> &z, const qp::direct::Ctrl<Real> &ctrl = qp::direct::Ctrl<Real>())¶

void QP(const DistSparseMatrix<Real> &Q, const DistSparseMatrix<Real> &A, const DistMultiVec<Real> &b, const DistMultiVec<Real> &c, DistMultiVec<Real> &x, DistMultiVec<Real> &y, DistMultiVec<Real> &z, const qp::direct::Ctrl<Real> &ctrl = qp::direct::Ctrl<Real>())¶

C API¶

Single-precision¶

ElError ElQPDirect_s(ElConstMatrix_s Q, ElConstMatrix_s A, ElConstMatrix_s b, ElConstMatrix_s c, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z)¶

ElError ElQPDirectDist_s(ElConstDistMatrix_s Q, ElConstDistMatrix_s A, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z)¶

ElError ElQPDirectSparse_s(ElConstSparseMatrix_s Q, ElConstSparseMatrix_s A, ElConstMatrix_s b, ElConstMatrix_s c, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z)¶

ElError ElQPDirectDistSparse_s(ElConstDistSparseMatrix_s Q, ElConstDistSparseMatrix_s A, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z)¶

Double-precision¶

ElError ElQPDirect_d(ElConstMatrix_d Q, ElConstMatrix_d A, ElConstMatrix_d b, ElConstMatrix_d c, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z)¶

ElError ElQPDirectDist_d(ElConstDistMatrix_d Q, ElConstDistMatrix_d A, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z)¶

ElError ElQPDirectSparse_d(ElConstSparseMatrix_d Q, ElConstSparseMatrix_d A, ElConstMatrix_d b, ElConstMatrix_d c, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z)¶

ElError ElQPDirectDistSparse_d(ElConstDistSparseMatrix_d Q, ElConstDistSparseMatrix_d A, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z)¶

Expert interfaces¶

Single-precision¶

ElError ElQPDirectX_s(ElConstMatrix_s Q, ElConstMatrix_s A, ElConstMatrix_s b, ElConstMatrix_s c, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElQPDirectCtrl_s ctrl)¶

ElError ElQPDirectXDist_s(ElConstDistMatrix_s Q, ElConstDistMatrix_s A, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z, ElQPDirectCtrl_s ctrl)¶

ElError ElQPDirectXSparse_s(ElConstSparseMatrix_s Q, ElConstSparseMatrix_s A, ElConstMatrix_s b, ElConstMatrix_s c, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElQPDirectCtrl_s ctrl)¶

ElError ElQPDirectXDistSparse_s(ElConstDistSparseMatrix_s Q, ElConstDistSparseMatrix_s A, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z, ElQPDirectCtrl_s ctrl)¶

Double-precision¶

ElError ElQPDirectX_d(ElConstMatrix_d Q, ElConstMatrix_d A, ElConstMatrix_d b, ElConstMatrix_d c, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElQPDirectCtrl_d ctrl)¶

ElError ElQPDirectXDist_d(ElConstDistMatrix_d Q, ElConstDistMatrix_d A, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z, ElQPDirectCtrl_d ctrl)¶

ElError ElQPDirectXSparse_d(ElConstSparseMatrix_d Q, ElConstSparseMatrix_d A, ElConstMatrix_d b, ElConstMatrix_d c, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElQPDirectCtrl_d ctrl)¶

ElError ElQPDirectXDistSparse_d(ElConstDistSparseMatrix_d Q, ElConstDistSparseMatrix_d A, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z, ElQPDirectCtrl_d ctrl)¶