No strong duality
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This example is interesting, because strong duality doesn't hold for the extensive form (see if you can show why!), but we still converge.
using SDDP, HiGHS, Test
function no_strong_duality()
model = SDDP.PolicyGraph(
SDDP.Graph(
:root,
[:node],
[(:root => :node, 1.0), (:node => :node, 0.5)],
);
optimizer = HiGHS.Optimizer,
lower_bound = 0.0,
) do sp, t
@variable(sp, x, SDDP.State, initial_value = 1.0)
@stageobjective(sp, x.out)
@constraint(sp, x.in == x.out)
end
SDDP.train(model)
@test SDDP.calculate_bound(model) ≈ 2.0 atol = 1e-5
return
end
no_strong_duality()
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SDDP.jl (c) Oscar Dowson and contributors, 2017-24
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problem
nodes : 1
state variables : 1
scenarios : Inf
existing cuts : false
options
solver : serial mode
risk measure : SDDP.Expectation()
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [3, 3]
AffExpr in MOI.EqualTo{Float64} : [1, 1]
VariableRef in MOI.GreaterThan{Float64} : [1, 1]
numerical stability report
matrix range [1e+00, 1e+00]
objective range [1e+00, 1e+00]
bounds range [0e+00, 0e+00]
rhs range [0e+00, 0e+00]
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iteration simulation bound time (s) solves pid
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1 1.000000e+00 1.500000e+00 1.598120e-03 3 1
40 4.000000e+00 2.000000e+00 4.288697e-02 578 1
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status : simulation_stopping
total time (s) : 4.288697e-02
total solves : 578
best bound : 2.000000e+00
simulation ci : 1.950000e+00 ± 5.568095e-01
numeric issues : 0
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