Affine Quadratic Programs¶

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

Python API¶

QPAffine(Q, A, G, b, c, h, x, y, z, s[, ctrl=None])¶

C++ API¶

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

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

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

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

C API¶

Single-precision¶

ElError ElQPAffine_s(ElConstMatrix_s Q, ElConstMatrix_s A, ElConstMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s)¶

ElError ElQPAffineDist_s(ElConstDistMatrix_s Q, ElConstDistMatrix_s A, ElConstDistMatrix_s G, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElConstDistMatrix_s h, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z, ElDistMatrix_s s)¶

ElError ElQPAffineSparse_s(ElConstSparseMatrix_s Q, ElConstSparseMatrix_s A, ElConstSparseMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s)¶

ElError ElQPAffineDistSparse_s(ElConstDistSparseMatrix_s Q, ElConstDistSparseMatrix_s A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElConstDistMultiVec_s h, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z, ElDistMultiVec_s s)¶

Double-precision¶

ElError ElQPAffine_d(ElConstMatrix_d Q, ElConstMatrix_d A, ElConstMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s)¶

ElError ElQPAffineDist_d(ElConstDistMatrix_d Q, ElConstDistMatrix_d A, ElConstDistMatrix_d G, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElConstDistMatrix_d h, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z, ElDistMatrix_d s)¶

ElError ElQPAffineSparse_d(ElConstSparseMatrix_d Q, ElConstSparseMatrix_d A, ElConstSparseMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s)¶

ElError ElQPAffineDistSparse_d(ElConstDistSparseMatrix_d Q, ElConstDistSparseMatrix_d A, ElConstDistSparseMatrix_d G, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElConstDistMultiVec_d h, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z, ElDistMultiVec_d s)¶

Expert interfaces¶

Single-precision¶

ElError ElQPAffineX_s(ElConstMatrix_s Q, ElConstMatrix_s A, ElConstMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s, ElQPAffineCtrl_s ctrl)¶

ElError ElQPAffineXDist_s(ElConstDistMatrix_s Q, ElConstDistMatrix_s A, ElConstDistMatrix_s G, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElConstDistMatrix_s h, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z, ElDistMatrix_s s, ElQPAffineCtrl_s ctrl)¶

ElError ElQPAffineXSparse_s(ElConstSparseMatrix_s Q, ElConstSparseMatrix_s A, ElConstSparseMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s, ElQPAffineCtrl_s ctrl)¶

ElError ElQPAffineXDistSparse_s(ElConstDistSparseMatrix_s Q, ElConstDistSparseMatrix_s A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElConstDistMultiVec_s h, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z, ElDistMultiVec_s s, ElQPAffineCtrl_s ctrl)¶

Double-precision¶

ElError ElQPAffineX_d(ElConstMatrix_d Q, ElConstMatrix_d A, ElConstMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s, ElQPAffineCtrl_d ctrl)¶

ElError ElQPAffineXDist_d(ElConstDistMatrix_d Q, ElConstDistMatrix_d A, ElConstDistMatrix_d G, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElConstDistMatrix_d h, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z, ElDistMatrix_d s, ElQPAffineCtrl_d ctrl)¶

ElError ElQPAffineXSparse_d(ElConstSparseMatrix_d Q, ElConstSparseMatrix_d A, ElConstSparseMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s, ElQPAffineCtrl_d ctrl)¶

ElError ElQPAffineXDistSparse_d(ElConstDistSparseMatrix_d Q, ElConstDistSparseMatrix_d A, ElConstDistSparseMatrix_d G, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElConstDistMultiVec_d h, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z, ElDistMultiVec_d s, ElQPAffineCtrl_d ctrl)¶