remove lambertW

Author: chriscoey

Project.toml

@@ -8,7 +8,6 @@ CodecBzip2 = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
 CodecZlib = "944b1d66-785c-5afd-91f1-9de20f533193"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JSONSchema = "7d188eb4-7ad8-530c-ae41-71a32a6d4692"
-LambertW = "984bce1d-4616-540c-a9ee-88d1112d94c9"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
 OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"

src/Bridges/Constraint/relentr_to_exp.jl

@@ -104,23 +104,13 @@ function MOI.get(model::MOI.ModelLike, attr::Union{MOI.ConstraintDual, MOI.Const
     return dual
 end
 # Given constraint dual start of (u, v, w), constraint dual on GreaterThan is u
-# and on exponential cone constraint i is (r,s,t) for -r exp (s/r - 1) = t, where
-# s = w_i, t = v_i, and r = exp(W(-s / (-t * e))) * (-t * e), where W is the
-# Lambert W function. The derivation of the r expression follows:
-# -r exp (s/r - 1) = t => s/r - 1 = log(t/-r) => s/r = log (e * t/-r)
-# => -s = r log (r / (-t * e)) => -s / (-t * e) = r / (-t * e) log (r / (-t * e))
-# let x = r / (-t * e) and y = -s / (-t * e), solve y = x log x using Lambert W function:
-# x = exp(W(y)) => r / (-t * e) = exp(W(-s / (-t * e))) => r = exp(W(-s / (-t * e))) * (-t * e).
-import LambertW
+# and on exponential cone constraint i is (r_i, w_i, v_i), but since y_i is free,
+# its dual is 0, so we have -r_i + value[1] == 0 hence r_i = value[1].
 function MOI.set(model::MOI.ModelLike, ::MOI.ConstraintDualStart, bridge::RelativeEntropyBridge, value)
     MOI.set(model, MOI.ConstraintDualStart(), bridge.ge_index, value[1])
     w_start = 1 + length(bridge.y)
     for i in eachindex(bridge.y)
-        s_value = value[w_start + i]
-        t_value = value[1 + i]
-        r_value = exp(LambertW.lambertw(s_value / (t_value * ℯ))) * -t_value * ℯ
-        @assert -r_value * exp(s_value / r_value - 1) - t_value ≈ 0
-        MOI.set(model, MOI.ConstraintDualStart(), bridge.exp_indices[i], [r_value, s_value, t_value])
+        MOI.set(model, MOI.ConstraintDualStart(), bridge.exp_indices[i], [value[1], value[w_start + i], value[1 + i]])
     end
     return
 end

test/Bridges/Constraint/relentr_to_exp.jl

@@ -1,6 +1,5 @@
 using Test
 
-import LambertW
 using MathOptInterface
 const MOI = MathOptInterface
 const MOIT = MathOptInterface.Test
@@ -89,9 +88,7 @@ config = MOIT.TestConfig()
         else
             @test MOI.get(mock, attr, greater[1]) == 2
             for i in 1:2
-                (s_value, t_value) = (value[3 + i], value[1 + i])
-                r_value = exp(LambertW.lambertw(s_value / (t_value * ℯ))) * -t_value * ℯ
-                @test MOI.get(mock, attr, exps[i]) == [r_value, s_value, t_value]
+                @test MOI.get(mock, attr, exps[i]) == [value[1], value[3 + i], value[1 + i]]
             end
         end
     end