Affine Second-Order Cone Programs¶

\[\begin{split}\min_{x,s} & \{\; c^T x \; | \; A x = b \;\wedge\; G x + s = h\;\wedge\; s \in \mathcal{K} \;\}, \\ \max_{y,z} & \{\; - b^T y - h^T z \; | \; A^T y + G^T z + c = 0 \;\wedge\; z \in \mathcal{K} \;\}\end{split}\]

In order to represent that product of second-order cones, the following routines accept two integer vectors which are of the same length as \(s\) and \(z\):

orders: The size of the subcone containing each entry of \(s\)
firstInds: The first index (counting from zero) of the subcone containing each entry of \(s\)

Python API¶

SOCPAffine(A, G, b, c, h, orders, firstInds, x, y, z, s[, ctrl=None])¶

C++ API¶

void SOCP(const Matrix<Real> &A, const Matrix<Real> &G, const Matrix<Real> &b, const Matrix<Real> &c, const Matrix<Real> &h, const Matrix<Int> &orders, const Matrix<Int> &firstInds, Matrix<Real> &x, Matrix<Real> &y, Matrix<Real> &z, Matrix<Real> &s, const socp::affine::Ctrl<Real> &ctrl = socp::affine::Ctrl<Real>())¶

void SOCP(const ElementalMatrix<Real> &A, const ElementalMatrix<Real> &G, const ElementalMatrix<Real> &b, const ElementalMatrix<Real> &c, const ElementalMatrix<Real> &h, const ElementalMatrix<Int> &orders, const ElementalMatrix<Int> &firstInds, ElementalMatrix<Real> &x, ElementalMatrix<Real> &y, ElementalMatrix<Real> &z, ElementalMatrix<Real> &s, const socp::affine::Ctrl<Real> &ctrl = socp::affine::Ctrl<Real>())¶

void SOCP(const SparseMatrix<Real> &A, const SparseMatrix<Real> &G, const Matrix<Real> &b, const Matrix<Real> &c, const Matrix<Real> &h, Matrix<Real> &x, const Matrix<Int> &orders, const Matrix<Int> &firstInds, Matrix<Real> &y, Matrix<Real> &z, Matrix<Real> &s, const socp::affine::Ctrl<Real> &ctrl = socp::affine::Ctrl<Real>())¶

void SOCP(const DistSparseMatrix<Real> &A, const DistSparseMatrix<Real> &G, const DistMultiVec<Real> &b, const DistMultiVec<Real> &c, const DistMultiVec<Real> &h, const DistMultiVec<Int> &orders, const DistMultiVec<Int> &firstInds, DistMultiVec<Real> &x, DistMultiVec<Real> &y, DistMultiVec<Real> &z, DistMultiVec<Real> &s, const socp::affine::Ctrl<Real> &ctrl = socp::affine::Ctrl<Real>())¶

C API¶

Single-precision¶

ElError ElSOCPAffine_s(ElConstMatrix_s A, ElConstMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s)¶

ElError ElSOCPAffineDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s G, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElConstDistMatrix_s h, ElConstDistMatrix_i orders, ElConstDistMatrix_i firstInds, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z, ElDistMatrix_s s)¶

ElError ElSOCPAffineSparse_s(ElConstSparseMatrix_s A, ElConstSparseMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s)¶

ElError ElSOCPAffineDistSparse_s(ElConstDistSparseMatrix_s A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElConstDistMultiVec_s h, ElConstDistMultiVec_i orders, ElConstDistMultiVec_i firstInds, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z, ElDistMultiVec_s s)¶

Double-precision¶

ElError ElSOCPAffine_d(ElConstMatrix_d A, ElConstMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s)¶

ElError ElSOCPAffineDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_s G, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElConstDistMatrix_d h, ElConstDistMatrix_i orders, ElConstDistMatrix_i firstInds, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z, ElDistMatrix_d s)¶

ElError ElSOCPAffineSparse_d(ElConstSparseMatrix_d A, ElConstSparseMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s)¶

ElError ElSOCPAffineDistSparse_d(ElConstDistSparseMatrix_d A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElConstDistMultiVec_d h, ElConstDistMultiVec_i orders, ElConstDistMultiVec_i firstInds, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z, ElDistMultiVec_d s)¶

Expert interfaces¶

Single-precision¶

ElError ElSOCPAffineX_s(ElConstMatrix_s A, ElConstMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s, ElSOCPAffineCtrl_s ctrl)¶

ElError ElSOCPAffineXDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s G, ElConstDistMatrix_s b, ElConstDistMatrix_s c, ElConstDistMatrix_s h, ElConstDistMatrix_i orders, ElConstDistMatrix_i firstInds, ElDistMatrix_s x, ElDistMatrix_s y, ElDistMatrix_s z, ElDistMatrix_s s, ElSOCPAffineCtrl_s ctrl)¶

ElError ElSOCPAffineXSparse_s(ElConstSparseMatrix_s A, ElConstSparseMatrix_s G, ElConstMatrix_s b, ElConstMatrix_s c, ElConstMatrix_s h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_s x, ElMatrix_s y, ElMatrix_s z, ElMatrix_s s, ElSOCPAffineCtrl_s ctrl)¶

ElError ElSOCPAffineXDistSparse_s(ElConstDistSparseMatrix_s A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_s b, ElConstDistMultiVec_s c, ElConstDistMultiVec_s h, ElConstDistMultiVec_i orders, ElConstDistMultiVec_i firstInds, ElDistMultiVec_s x, ElDistMultiVec_s y, ElDistMultiVec_s z, ElDistMultiVec_s s, ElSOCPAffineCtrl_s ctrl)¶

Double-precision¶

ElError ElSOCPAffineX_d(ElConstMatrix_d A, ElConstMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s, ElSOCPAffineCtrl_d ctrl)¶

ElError ElSOCPAffineXDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_s G, ElConstDistMatrix_d b, ElConstDistMatrix_d c, ElConstDistMatrix_d h, ElConstDistMatrix_i orders, ElConstDistMatrix_i firstInds, ElDistMatrix_d x, ElDistMatrix_d y, ElDistMatrix_d z, ElDistMatrix_d s, ElSOCPAffineCtrl_d ctrl)¶

ElError ElSOCPAffineXSparse_d(ElConstSparseMatrix_d A, ElConstSparseMatrix_d G, ElConstMatrix_d b, ElConstMatrix_d c, ElConstMatrix_d h, ElConstMatrix_i orders, ElConstMatrix_i firstInds, ElMatrix_d x, ElMatrix_d y, ElMatrix_d z, ElMatrix_d s, ElSOCPAffineCtrl_d ctrl)¶

ElError ElSOCPAffineXDistSparse_d(ElConstDistSparseMatrix_d A, ElConstDistSparseMatrix_s G, ElConstDistMultiVec_d b, ElConstDistMultiVec_d c, ElConstDistMultiVec_d h, ElConstDistMultiVec_i orders, ElConstDistMultiVec_i firstInds, ElDistMultiVec_d x, ElDistMultiVec_d y, ElDistMultiVec_d z, ElDistMultiVec_d s, ElSOCPAffineCtrl_d ctrl)¶