Implement set_start_value for constraint indices

[blegat]

Should it be set_start_value or set_primal_start_value given that for the dual it's set_dual_start_value and for variables it is set_start_value ?

cc @kalmarek

[kalmarek]

I'm not sure where to report this error, so I'll do it here.

Env:

JuMP-0.22.2
SCS-0.8.2 or SCS-0.9.0

MWE:

using JuMP
using SCS

function setwarmstart!(model::JuMP.Model, warmstart)
    constraint_map = Dict(
        ct => JuMP.all_constraints(model, ct...) for
        ct in JuMP.list_of_constraint_types(model)
    )

    JuMP.set_start_value.(JuMP.all_variables(model), warmstart.primal)

    for (ct, idx) in pairs(constraint_map)
        JuMP.set_start_value.(idx, warmstart.slack[ct])
        JuMP.set_dual_start_value.(idx, warmstart.dual[ct])
    end
    return model
end

function getwarmstart(model::JuMP.Model)
    constraint_map = Dict(
        ct => JuMP.all_constraints(model, ct...) for
        ct in JuMP.list_of_constraint_types(model)
    )

    primal = value.(JuMP.all_variables(model))

    slack = Dict(k => value.(v) for (k, v) in constraint_map)
    duals = Dict(k => JuMP.dual.(v) for (k, v) in constraint_map)

    return (primal = primal, dual = duals, slack = slack)
end

using Random
using SparseArrays

let (m, n, k) = (5, 10, 3)
    Random.seed!(123)
    A = rand(m, n)
    b = A * rand(n)
    c = rand(n)
    Bp = rand(1:n, k, k)
    B = rand(k, k)

    model = Model(optimizer_with_attributes(SCS.Optimizer, "warm_start" => true))
    @variable(model, x[1:n] >= 0.0)
    @constraint(model, A * x .== b)

    @objective(model, Min, c'x)
    optimize!(model)

    warmstart = getwarmstart(model)

    model2 = setwarmstart!(model, warmstart)
    optimize!(model2)
end

results in warmstarting just fine, however if I add a psd constraint like this:

@constraint(model, B.*x[Bp] in PSDCone())

setwarmstart! throws

ERROR: MathOptInterface.UnsupportedAttribute{MathOptInterface.ConstraintPrimalStart}: Attribute MathOptInterface.ConstraintPrimalStart() is not supported by the model.
Stacktrace:
  [1] set(model::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, attr::MathOptInterface.ConstraintPrimalStart, bridge::MathOptInterface.Bridges.Constraint.SquareBridge{Float64, MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeTriangle, MathOptInterface.PositiveSemidefiniteConeSquare}, value::Vector{Float64})
    @ MathOptInterface.Bridges ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge.jl:127
  [2] (::MathOptInterface.Bridges.var"#3#4"{typeof(MathOptInterface.set), MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.ConstraintPrimalStart, Tuple{Vector{Float64}}})(bridge::MathOptInterface.Bridges.Constraint.SquareBridge{Float64, MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeTriangle, MathOptInterface.PositiveSemidefiniteConeSquare})
    @ MathOptInterface.Bridges ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:308
  [3] (::MathOptInterface.Bridges.var"#1#2"{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, MathOptInterface.Bridges.var"#3#4"{typeof(MathOptInterface.set), MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.ConstraintPrimalStart, Tuple{Vector{Float64}}}})()
    @ MathOptInterface.Bridges ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:293
  [4] call_in_context(map::MathOptInterface.Bridges.Variable.Map, bridge_index::Int64, f::MathOptInterface.Bridges.var"#1#2"{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, MathOptInterface.Bridges.var"#3#4"{typeof(MathOptInterface.set), MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.ConstraintPrimalStart, Tuple{Vector{Float64}}}})
    @ MathOptInterface.Bridges.Variable ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/Variable/map.jl:455
  [5] call_in_context
    @ ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/Variable/map.jl:486 [inlined]
  [6] call_in_context
    @ ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:290 [inlined]
  [7] call_in_context
    @ ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:305 [inlined]
  [8] _set_substituted(b::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, attr::MathOptInterface.ConstraintPrimalStart, ci::MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, value::Vector{Float64})
    @ MathOptInterface.Bridges ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:1278
  [9] set
    @ ~/.julia/packages/MathOptInterface/eoIu0/src/Bridges/bridge_optimizer.jl:1291 [inlined]
 [10] set(m::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, attr::MathOptInterface.ConstraintPrimalStart, index::MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, value::Vector{Float64})
    @ MathOptInterface.Utilities ~/.julia/packages/MathOptInterface/eoIu0/src/Utilities/cachingoptimizer.jl:760
 [11] set(model::Model, attr::MathOptInterface.ConstraintPrimalStart, cr::ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, SquareMatrixShape}, value::Vector{Float64})
    @ JuMP ~/.julia/packages/JuMP/lnUbA/src/JuMP.jl:1321
 [12] set_start_value(con_ref::ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}, SquareMatrixShape}, value::Matrix{Float64})
    @ JuMP ~/.julia/packages/JuMP/lnUbA/src/constraints.jl:148
 [13] _broadcast_getindex_evalf
    @ ./broadcast.jl:670 [inlined]
 [14] _broadcast_getindex
    @ ./broadcast.jl:643 [inlined]
 [15] getindex
    @ ./broadcast.jl:597 [inlined]
 [16] macro expansion
    @ ./broadcast.jl:961 [inlined]
 [17] macro expansion
    @ ./simdloop.jl:77 [inlined]
 [18] copyto!
    @ ./broadcast.jl:960 [inlined]
 [19] copyto!
    @ ./broadcast.jl:913 [inlined]
 [20] copy
    @ ./broadcast.jl:885 [inlined]
 [21] materialize(bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(set_start_value), Tuple{Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.VectorAffineFunction{Float64}, MathOptInterface.PositiveSemidefiniteConeSquare}}}, Vector{Matrix{Float64}}}})
    @ Base.Broadcast ./broadcast.jl:860
 [22] setwarmstart!(model::Model, warmstart::NamedTuple{(:primal, :dual, :slack), Tuple{Vector{Float64}, Dict{Tuple{DataType, DataType}, Vector}, Dict{Tuple{DataType, DataType}, Vector}}})
    @ Main ./REPL[5]:10
 [23] top-level scope
    @ REPL[11]:20

any help would be much appreciated

[odow]

Okay. It works if you have @constraint(model, Symmetric(B.*x[Bp]) in PSDCone()), so we're missing a method to pass start values in the bridge between a square PSD cone and a triangular PSD cone.

We should open an issue in MOI.