[WIP] Support convex qp

[klamike]

closes #28

Used claude for this.

I plan to make a PR after this that renames milp to prog. Kept it as is to make it slightly easier to review.

[codecov]

Codecov Report

❌ Patch coverage is 81.90955% with 36 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/problems/program.jl	74.50%	13 Missing ⚠️
src/problems/modify.jl	61.11%	7 Missing ⚠️
src/components/preconditioning.jl	75.00%	4 Missing ⚠️
src/components/step_size.jl	82.60%	4 Missing ⚠️
src/components/permutation.jl	50.00%	2 Missing ⚠️
src/algorithms/common.jl	50.00%	1 Missing ⚠️
src/algorithms/pdlp.jl	93.33%	1 Missing ⚠️
src/components/errors.jl	94.44%	1 Missing ⚠️
src/problems/solution.jl	66.66%	1 Missing ⚠️
src/utils/device.jl	75.00%	1 Missing ⚠️
... and 1 more

Files with missing lines	Coverage Δ
src/CoolPDLP.jl	100.00% <ø> (ø)
src/MOI_wrapper.jl	97.46% <100.00%> (+0.43%)	⬆️
src/algorithms/pdhg.jl	90.24% <100.00%> (+0.24%)	⬆️
src/components/conversion.jl	60.00% <ø> (ø)
src/components/scratch.jl	100.00% <100.00%> (ø)
src/utils/test.jl	97.29% <100.00%> (ø)
src/algorithms/common.jl	81.63% <50.00%> (ø)
src/algorithms/pdlp.jl	91.95% <93.33%> (+0.18%)	⬆️
src/components/errors.jl	76.47% <94.44%> (+3.29%)	⬆️
src/problems/solution.jl	76.92% <66.66%> (-1.46%)	⬇️
... and 7 more

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[gdalle]

I'll take a closer look at #21 first before reviewing this one,
Thanks for your hard work!

[klamike]

Sure! If you choose to accept I can update this branch to use that convention too.