Moving from LMI toolbox (Matlab) to JuliaOpt

Does anyone have experience in moving from Matlab’s LMI toolbox to the various JuliaOpt packages? I’m taking a non-linear dynamics course (AAE666 at Purdue) and we’ve just been introduced to linear matrix inequalities in the context of quadratic stability. As such, I’m still trying to grapple with the toolbox and LMIs in general and I’m not sure how to translate such a problem to a JuliaOPT package. Any resources or thoughts would be much appreciated.

1 Like

Did you have a look at JuMP, especially the Section Semidefinite Constraints or the Example Example minimal Ellipse?
I have no experience so far in LMI’s but I think this would be a good starting point.

For example solving the Lyapunov Inequality for a continuous system could look like this:

using JuMP
using MosekTools
using LinearAlgebra

A = [-0.5 1; 0 -0.3]; n = size(A,1); Q = [1 0; 0 1]
model = Model(with_optimizer(Mosek.Optimizer))
@variable(model, P[i=1:n, j=1:n], PSD)
@SDconstraint(model, P ⪰ 0)
@SDconstraint(model, A'*P + P*A ⪯ -Q)
@SDconstraint(model, A'*P + P*A ⪰ -Q)
optimize!(model)
P = value.(P)
# Test result:
A'*P + P*A ≈ -Q
1 Like

I wanted to try the example in the above post with a different optimizer. But, I got a StactOverflowError. Any ideas what I am doing wrong?

using JuMP
using SCS
using LinearAlgebra 

A = [-0.5 1; 0 -0.3] 
n = size(A,1)
Q = [1 0; 0 1.]
model = Model(with_optimizer(SCS.Optimizer))
@variable(model, P[1:n, 1:n], PSD)
@SDconstraint(model, P ⪰ 0)
@SDconstraint(model, A'*P + P*A ≥ -Q)
@SDconstraint(model, A'*P + P*A ≤ -Q)
optimize!(model)
P = value.(P)
# Test result:
A'*P + P*A ≈ -Q
ERROR: LoadError: StackOverflowError:
Stacktrace:
 [1] mutable_operate!(::typeof(MutableArithmetics.sub_mul), ::Matrix{AffExpr}, ::Matrix{VariableRef}, ::Matrix{Float64}) (repeats 79984 times)
   @ MutableArithmetics ~/.julia/packages/MutableArithmetics/bPWR4/src/linear_algebra.jl:132

How about using Convex.jl?

julia> using Convex, SCS, LinearAlgebra

julia> A = [-0.5 1; 0 -0.3]
2×2 Matrix{Float64}:
 -0.5   1.0
  0.0  -0.3

julia> n = size(A,1)
2

julia> eigvals(A)
2-element Vector{Float64}:
 -0.5
 -0.3

julia> X = Semidefinite(n)
Variable
size: (2, 2)
sign: real
vexity: affine
id: 404…993

julia> constraint = A'*X + X*A ⪯ -Matrix{Float64}(I, n, n)
sdp constraint (affine)
└─ + (affine; real)
   ├─ 2×2 Matrix{Float64}
   └─ - (affine; real)
      └─ + (affine; real)
         ├─ …
         └─ …

julia> problem = satisfy(constraint)
minimize
└─ 0
subject to
└─ sdp constraint (affine)
   └─ + (affine; real)
      ├─ 2×2 Matrix{Float64}
      └─ - (affine; real)
         └─ …

status: `solve!` not called yet

julia> solve!(problem,() -> SCS.Optimizer(verbose=false))

julia> problem.status
OPTIMAL::TerminationStatusCode = 1

julia> X.value
2×2 Matrix{Float64}:
 1.83577   2.88281
 2.88281  11.9403

julia> eigvals(X.value)
2-element Vector{Float64}:
  1.071158392495276
 12.704883497869783

2 Likes

Someone asked this yesterday on StackOverflow: optimization - Julia JuMP StackOverflow Error when defining a constraint on linear matrix inequalities - Stack Overflow

It’s a bug: Stackoverflow in SDconstraint · Issue #86 · jump-dev/MutableArithmetics.jl · GitHub

As a work-around, split it into an expression first:

@expression(model, ex, A' * P + P * A)
@SDconstraint(model, ex <= -Q)
2 Likes

@zdenek_hurak Thank you for pointing out Convex.jl and providing me with the example.

@odow Thank you for the workaround. It works :smile:

If you update your packages, is this fixed now? If not, can you provide the output of ] st -m.

The problem is fixed after the update. After the update, MutableArithmetics package is upgraded from v.0.2.14 to v.0.2.15. The problem is fixed already, but in case you are interested, here is the output of ]st -m

(@dev-env) pkg> st -m
      Status `~/.julia/environments/dev-env/Manifest.toml`
  [c3fe647b] AbstractAlgebra v0.15.1
  [621f4979] AbstractFFTs v1.0.1
  [537997a7] AbstractPlotting v0.15.27
  [1520ce14] AbstractTrees v0.3.4
  [79e6a3ab] Adapt v3.3.0
  [27a7e980] Animations v0.4.1
  [c7e460c6] ArgParse v1.1.3
  [ec485272] ArnoldiMethod v0.1.0
  [4fba245c] ArrayInterface v3.1.7
  [4c555306] ArrayLayouts v0.6.5
  [bf4720bc] AssetRegistry v0.1.0
  [13072b0f] AxisAlgorithms v1.0.0
  [aae01518] BandedMatrices v0.16.8
  [6e4b80f9] BenchmarkTools v0.5.0
  [9e28174c] BinDeps v1.0.2
  [b99e7846] BinaryProvider v0.5.10
  [ad839575] Blink v0.12.5
  [8e7c35d0] BlockArrays v0.15.2
  [a74b3585] Blosc v0.7.0
  [764a87c0] BoundaryValueDiffEq v2.7.1
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  [49dc2e85] Calculus v0.5.1
  [324d7699] CategoricalArrays v0.9.5
  [c45f814d] Causal v0.3.0 `~/.julia/dev/Causal`
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  [b6b21f68] Ipopt v0.6.5
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  [c8e1da08] IterTools v1.3.0
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  [42fd0dbc] IterativeSolvers v0.9.0
  [82899510] IteratorInterfaceExtensions v1.0.0
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  [97c1335a] JSExpr v0.5.2
  [682c06a0] JSON v0.21.1
  [7d188eb4] JSONSchema v0.3.3
  [4076af6c] JuMP v0.21.6
  [aa1ae85d] JuliaInterpreter v0.8.11
  [5ab0869b] KernelDensity v0.6.2
  [b964fa9f] LaTeXStrings v1.2.1
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  [dbb5928d] MappedArrays v0.3.0
  [7eb4fadd] Match v1.1.0
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  [fb77eaff] Sundials_jll v5.2.0+1
  [b47fdcd6] TetGen_jll v1.5.1+1
  [a2964d1f] Wayland_jll v1.17.0+4
  [2381bf8a] Wayland_protocols_jll v1.18.0+4
  [02c8fc9c] XML2_jll v2.9.11+0
  [aed1982a] XSLT_jll v1.1.33+4
  [4f6342f7] Xorg_libX11_jll v1.6.9+4
  [0c0b7dd1] Xorg_libXau_jll v1.0.9+4
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.3+4
  [1082639a] Xorg_libXext_jll v1.3.4+4
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.0+3
  [c7cfdc94] Xorg_libxcb_jll v1.13.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.0+4
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.2+4
  [33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
  [c5fb5394] Xorg_xtrans_jll v1.4.0+3
  [8f1865be] ZeroMQ_jll v4.3.2+6
  [3161d3a3] Zstd_jll v1.4.8+0
  [28df3c45] boost_jll v1.71.0+3
  [9a68df92] isoband_jll v0.2.2+0
  [0ac62f75] libass_jll v0.14.0+4
  [e9ad47b2] libcgal_julia_jll v0.16.106+0
  [3eaa8342] libcxxwrap_julia_jll v0.8.6+0
  [f638f0a6] libfdk_aac_jll v0.1.6+4
  [b53b4c65] libpng_jll v1.6.37+6
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.6+6
  [1270edf5] x264_jll v2020.7.14+2
  [dfaa095f] x265_jll v3.0.0+3
  [d8fb68d0] xkbcommon_jll v0.9.1+5
  [0dad84c5] ArgTools
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8bb1440f] DelimitedFiles
  [8ba89e20] Distributed
  [f43a241f] Downloads
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions
  [44cfe95a] Pkg
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML
  [a4e569a6] Tar
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll
  [781609d7] GMP_jll
  [deac9b47] LibCURL_jll
  [29816b5a] LibSSH2_jll
  [3a97d323] MPFR_jll
  [c8ffd9c3] MbedTLS_jll
  [14a3606d] MozillaCACerts_jll
  [4536629a] OpenBLAS_jll
  [bea87d4a] SuiteSparse_jll
  [83775a58] Zlib_jll
  [8e850ede] nghttp2_jll
  [3f19e933] p7zip_jll

(@dev-env) pkg> 
1 Like

Great! I had fixed this a while ago, it just needed a new release.

1 Like