WIP: First version of Polyhedral with QPDAS solver #76

mfalt · 2019-03-27T19:56:31Z

QPDAS is still not registered so the tests will fail (but pass locally).

I ran a simple benchmark with vectors of length 1000, 50 equality, and 50 inequality constraints and no constraints on the vector itself. The benchmark results, running https://gist.github.com/mfalt/465969600b27a4ec285ab67c2530d374
are:

Setup OSQP
  0.015556 seconds (95 allocations: 2.365 MiB)
Setup QPDAS
  0.000734 seconds (128 allocations: 1.539 MiB)
First prox OSQP:
  0.698441 seconds (16 allocations: 25.938 KiB)
First prox QPDAS:
  0.000935 seconds (1.19 k allocations: 336.773 KiB)
100 prox! OSQP:
 68.826197 seconds (1.60 k allocations: 3.297 MiB)
100 prox! QPDAS:
  0.420764 seconds (591.76 k allocations: 38.232 MiB, 0.64% gc time)

Note that performance is worse when adding upper and lower constraints on the vector itself, I haven't tested how it compares to osqp in this case yet.

mfalt · 2019-03-27T19:57:48Z

src/functions/indPolyhedralQPDAS.jl

+             u[upper_and_lower] ]
+
+    IndPolyhedralQPDAS{R}(Aeq, beq, Cieq, dieq)
+end


This function is quite nasty, but I don't see another way to support the old syntax otherwise.

It’s okay, I don’t see many other way of doing it.

I’m open to changing the overall syntax for the construction of IndPolyhedral objects. But maybe we can open a dedicated issue for that and focus here in meeting the current construction signature.

mfalt · 2019-03-27T19:59:26Z

Didn't mean to push the benchmark, will remove those.
This PR solves part of #52 (again)

lostella

Thank you! Benchmark results are impressive, good job with the solver!

Could you also update IndPolyhedral as part of this, and add the option for using this variant? Also, the docstring for IndPolyhedral could be updated with the solver argument and a brief description of the available options for it. I believe I didn’t do this before since OSQP was the only option there.

QPDAS is already on its way to be registered?

lostella · 2019-03-27T21:57:26Z

src/functions/indPolyhedralQPDAS.jl

+    IndPolyhedralQPDAS(A, C, b, d)
+
+```math
+S = \\{x : \\langle A, x \\rangle = b\\ ∧ \\langle C, x \\rangle \\le b\\}.


I would write Ax and Cx without angular parentheses (we use those everywhere else for inner products)

You're right, I just copied or from somewhere and forgot to change that.

lostella · 2019-03-27T22:00:30Z

src/functions/indPolyhedralQPDAS.jl

+function (f::IndPolyhedralQPDAS{R})(x::AbstractVector{R}) where R
+    Ax = f.A * x
+    Cx = f.C * x
+    return all(Ax .<= f.b .& Cx .<= f.d) ? R(0) : Inf


Is it Ax .== f.b here? Or rather isapprox.(Ax, f.b).

If this was a bug and no test failed, maybe a test is missing

Bug, will fix and add test.

lostella · 2019-03-27T22:11:57Z

src/functions/indPolyhedralQPDAS.jl

+             u[upper_and_lower] ]
+
+    IndPolyhedralQPDAS{R}(Aeq, beq, Cieq, dieq)
+end


It’s okay, I don’t see many other way of doing it.

I’m open to changing the overall syntax for the construction of IndPolyhedral objects. But maybe we can open a dedicated issue for that and focus here in meeting the current construction signature.

mfalt · 2019-03-28T19:35:17Z

Could you also update IndPolyhedral as part of this, and add the option for using this variant?

This should already be in the PR, or did you mean something else?

Also, the docstring for IndPolyhedral could be updated with the solver argument and a brief description of the available options for it. I believe I didn’t do this before since OSQP was the only option there.

Will do

QPDAS is already on its way to be registered?

I opened it to the public yesterday, wanted to test it against osqp here first. Will probably request it to be registered this weekend.

I will also post some more benchmarks, it seems like it is consistently 2x to 3000x faster than osqp for a wide variety of projection problems. So we should probably considering to make it the new dafault, maybe through some deprecation? (Trying to not be too partial here)

lostella · 2019-03-29T08:38:51Z

Yes sorry, it’s already in this PR, I was probably checking in master by mistake.

I’m open to changing the default, let’s maybe look into a more extensive comparison for this type of projections, including ill-conditioned problems where some solvers may have a hard time.

By the way, are you aware of any other open source QP solvers with Julia bindings (or pure Julia ones, even better)? Because when I was looking into this, I could only find OSQP, which was also very young back then.

mfalt · 2019-03-29T10:09:39Z

I’m open to changing the default, let’s maybe look into a more extensive comparison for this type of projections, including ill-conditioned problems where some solvers may have a hard time.

I completely agree, I'm currently running tests for large problems (its currently at 10_000 variables, 2000 equality, 2000inequality, osqp takes 2hours, qpdas 20min (doing 10 consecutive proxes on similar points). In this case I think the dual is quite ill-conditioned, do you have some good tips for generating ill-conditioned problems?

By the way, are you aware of any other open source QP solvers with Julia bindings (or pure Julia ones, even better)? Because when I was looking into this, I could only find OSQP, which was also very young back then.

Not really, at least not active-set solvers. qpOASES has similar performance as QPDAS, but it is in C++, and I was unable to write a working wrapper since it keeps variables in memory internally.

mfalt · 2019-04-04T15:01:59Z

The benchmarks for random problems with bounds either as lb <= Ax <= ub, (denoted u+l) and Ax <= ub (u) are as follows on my computer, for n=100 to 10000 variables:

where the ratios of the timings:

Note that QPDAS is faster in almost all cases, except when the number of variables is 5000 or 10000, and there are 2500 and 5000 upper and lower constraints respectively. However, osqp takes 2.2 and 11 hours to do init + 11proxes, and qpdas 0.5 and 8 hours in these cases, so I am not sure it is relevant for this package.

I will try to generate more tests for ill-conditioned problems when I have time.

First version of polyhedral with QPDAS

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mfalt requested a review from lostella March 27, 2019 19:56

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WIP: First version of Polyhedral with QPDAS solver #76

WIP: First version of Polyhedral with QPDAS solver #76

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mfalt commented Apr 4, 2019

WIP: First version of Polyhedral with QPDAS solver #76

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WIP: First version of Polyhedral with QPDAS solver #76

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