I'm using osqp-eigen v0.7.0, wondering if Hessian Matrix is supporting only symmetric matrix, rather than upper triangular matrix.

[Rem]

My partial code as follows:

// symmetric matrix
for (int i = 0; i < n - 1; ++i)
{
    hessian.insert(i, i + 1) = 1.0;
    hessian.insert(i + 1, i) = 1.0;
}
// upper triangular matrix
for (int i = 0; i < n - 1; ++i)
{
    hessian.insert(i, i + 1) = 2.0;
}

When I used the symmetric matrix, I got the true solution(I guess). Instead, solver return
status: problem non convex
while using upper triangular matrix.

[Silvio Traversaro]

Strictly speaking according to the documentation the hessian matrix is required to be symmetric, but looking in the code actually only an upper triangular view is used (see

osqp-eigen/include/OsqpEigen/Data.tpp

Lines 40 to 44 in a752c5e

 // set the hessian matrix 
 //  osqp 0.6.0 required only the upper triangular part of the hessian matrix 
 Derived hessianMatrixUpperTriangular = hessianMatrix.template triangularView<Eigen::Upper>(); 
 if (!OsqpEigen::SparseMatrixHelper::createOsqpSparseMatrix(hessianMatrixUpperTriangular, 
                                                            m_data->P)) 

), even if this behavior is not part of the public docs so it could change without notice.

Are you sure that in your example you are actually passing the two matrices in the two cases? Can you provide a full example in the two cases, instead an incomplete snippet of code? Thanks!

[Stefano Dafarra]

Hi @ZhiDaoYongYuan, did you fill the diagonal as well? If $n=2$, the corresponding matrix would be

$$\begin{bmatrix} 0 & 2 \\\ 2 & 0 \end{bmatrix}$$

whose eigenvalues are +2 and -2. Hence the matrix would not be positive semidefinite. So I would say that the error message is correct. I am not sure why it did not print it in the first case.