# How to implment \`logsumexp\` function in JuMP?

**URL:** <https://discourse.julialang.org/t/how-to-implment-logsumexp-function-in-jump/84376>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, differentiation, autodiff\
**Created:** [July 18, 2022, 4:35am UTC](https://discourse.julialang.org/t/how-to-implment-logsumexp-function-in-jump/84376 "2022-07-18T04:35:27Z")\
**Posts on this page:** 1\
**Showing post:** 6

<div class="post-metadata">

**Author:** ![iHany](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ihany/32/18151_2.png) [@iHany](https://discourse.julialang.org/u/iHany)\
**Post date:** [July 18, 2022, 5:38am UTC](https://discourse.julialang.org/t/how-to-implment-logsumexp-function-in-jump/84376/6 "2022-07-18T05:38:32Z")

</div>

And as your advice, I tried to convert it to an equivalent exponential cone program manually but it seems not to work and I’m kinda stuck with it

```julia
using ParametrisedConvexApproximators
using JuMP
import DiffOpt
import SCS
import ChainRulesCore
import Flux
using Convex
using UnPack

function main()
    model = Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
    empty!(model)
    set_silent(model)
    n, m, d = 3, 2, 1
    i_max = 20
    T = 1e-0
    h_array = [64]
    act = Flux.relu
    plse = PLSE(n, m, i_max, T, h_array, act)
    x = rand(n, d)
    @show plse(x, rand(m, d))
    u_star = infer_test(plse)
    return u_star
end

function infer_test(nn::PLSE)
    n, m, d = 3, 2, 1
    model = Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
    @variable(model, u[1:m])

    @unpack T = nn
    x = rand(n, d)
    tmp = ParametrisedConvexApproximators.affine_map(nn, x, u)
    # @NLobjective(model, Min, T * log(sum(exp((1/T)*tmp[i]) for i in 1:nn.i_max)))
    # equivalent form of logsumexp
    _tmp = (1/T) * tmp
    @variable(model, v[1:nn.i_max])
    @variable(model, t)
    @constraint(model, sum(v) <= 1)
    @constraint(model, [i=1:nn.i_max], [v[i], 1, _tmp[i, 1] - t] in MOI.ExponentialCone())
    @objective(model, Min, T*t)
    optimize!(model)
    return value.(u)
end

```

gives

```julia
julia> main()
plse(x, rand(m, d)) = [3.00289608300575;;]
ERROR: Constraints of type MathOptInterface.VectorAffineFunction{Float64}-in-MathOptInterface.ExponentialCone are not supported by the solver.

If you expected the solver to support your problem, you may have an error in your formulation. Otherwise, consider using a different solver.

The list of available solvers, along with the problem types they support, is available at https://jump.dev/JuMP.jl/stable/installation/#Supported-solvers.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] _moi_add_constraint(model::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.Optimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, f::MathOptInterface.VectorAffineFunction{Float64}, s::MathOptInterface.ExponentialCone)
    @ JuMP ~/.julia/packages/JuMP/2IF9U/src/constraints.jl:534
  [3] add_constraint(model::Model, con::VectorConstraint{AffExpr, MathOptInterface.ExponentialCone, VectorShape}, name::String)
    @ JuMP ~/.julia/packages/JuMP/2IF9U/src/constraints.jl:560
  [4] macro expansion
    @ ~/.julia/packages/JuMP/2IF9U/src/macros.jl:814 [inlined]
  [5] (::var"#228#232"{VariableRef, Vector{VariableRef}, Matrix{AffExpr}, Model})(i::Int64)
    @ Main ~/.julia/dev/ParametrisedConvexApproximators/test/tmp.jl:27
  [6] #37
    @ ~/.julia/packages/JuMP/2IF9U/src/Containers/container.jl:72 [inlined]
  [7] iterate
    @ ./generator.jl:47 [inlined]
  [8] collect(itr::Base.Generator{JuMP.Containers.VectorizedProductIterator{Tuple{Base.OneTo{Int64}}}, JuMP.Containers.var"#37#38"{var"#228#232"{VariableRef, Vector{VariableRef}, Matrix{AffExpr}, Model}}})
    @ Base ./array.jl:724
  [9] map(f::Function, A::JuMP.Containers.VectorizedProductIterator{Tuple{Base.OneTo{Int64}}})
    @ Base ./abstractarray.jl:2896
 [10] container
    @ ~/.julia/packages/JuMP/2IF9U/src/Containers/container.jl:72 [inlined]
 [11] container
    @ ~/.julia/packages/JuMP/2IF9U/src/Containers/container.jl:66 [inlined]
 [12] infer_test(nn::PLSE)
    @ Main ~/.julia/dev/ParametrisedConvexApproximators/test/tmp.jl:41
 [13] main()
    @ Main ~/.julia/dev/ParametrisedConvexApproximators/test/tmp.jl:23
 [14] top-level scope
    @ REPL[10]:1
 [15] top-level scope
    @ ~/.julia/packages/CUDA/sCev8/src/initialization.jl:52

```

---

_[View the full topic](https://discourse.julialang.org/t/how-to-implment-logsumexp-function-in-jump/84376)._