Evaluation of dual feasibility

[TomasOberhuber]

I have a question about the computation of the dual feasibility in your code. We need to evaluate

q * y + l * lambda^+ - u* lambda^-

where lambda is projection of c - K^T * y to the space Lambda.

We first compute c - K^Ty

cuPDLP-C/cupdlp/cupdlp_solver.c

Line 87 in 7b94c41

cupdlp_dual_feasibility_kernel_1_cuda(dualResidual, aty,

Next we need to compute compute the projection to the space Lambda which is here

cuPDLP-C/cupdlp/cupdlp_solver.c

Line 90 in 7b94c41

cupdlp_dual_feasibility_kernel_2_cuda(dSlackPos, dualResidual,

and here

cuPDLP-C/cupdlp/cupdlp_solver.c

Line 97 in 7b94c41

cupdlp_dual_feasibility_kernel_3_cuda(dSlackNeg, dualResidual,

I do not understand why do you use two vectors dSlackPos and dSlackNeg since thge result should be representable just by one vector lambda. But especially I am not sure about the line

cuPDLP-C/cupdlp/cuda/cupdlp_cuda_kernels.cu

Line 41 in 7b94c41

z[i] = -min(dualResidual[i], 0.0) * hasUpper[i];

Why is there the minus sign on front of min in the computation dSlackNeg? You then compute u*lambda^+ using

cuPDLP-C/cupdlp/cupdlp_solver.c

Line 100 in 7b94c41

cupdlp_dot(work, lp->nCols, dSlackNeg, resobj->dUpperFiltered, &temp);

and after that you subtract from dDualObj

cuPDLP-C/cupdlp/cupdlp_solver.c

Line 101 in 7b94c41

*dDualObj -= temp;

So it seems to me that you have two minus signs in your code instead of just one.