Hi,

I’m solving a problem through Convex.jl & COSMO.jl. I want to build a BigFloat version of the same problem to refine the solution, and i’d like to warm start it with the low-precision solution. For the dummy problem that I expose here, it might not make sense, but for some kind of hard QP or hard SOCP that i deal with, it does.

Here is what i tried yet:

```
using Convex, COSMO
y = Variable(3)
x = [1.0,2,3]
p = minimize(Convex.norm(y - x,2) + Convex.norm(y,1))
solve!(p, () -> COSMO.Optimizer(verbose=true),warmstart=true)
# Now find a better value with BigFloats (or other multi-precision type)
BigType = BigFloat # Or DoubleFloats.Double64, or MultiFloats.Float64x4...
x = BigType.(x)
set_value!(y,BigType.(Convex.evaluate(y)))
opt = COSMO.Optimizer{BigType}(verbose=true)
p = minimize(Convex.norm(y - x,2) + Convex.norm(y,1))
solve!(p, () -> opt,warmstart=true) # Errors with the following stacktrace:
```

```
julia> solve!(p, () -> opt,warmstart=true)
ERROR: MethodError: no method matching warm_start_primal!(::COSMO.Workspace{BigFloat}, ::Float64, ::Int64)
Closest candidates are:
warm_start_primal!(::COSMO.Workspace{T}, ::T, ::Integer) where T at C:\Users\u009192\.julia\packages\COSMO\Sb5eV\src\interface.jl:130
warm_start_primal!(::COSMO.Workspace{T}, ::Vector{T}, ::Union{Nothing, UnitRange{Int64}}) where T<:AbstractFloat at C:\Users\u009192\.juli
a\packages\COSMO\Sb5eV\src\interface.jl:128
warm_start_primal!(::COSMO.Workspace{T}, ::AbstractVector{T}) where T<:AbstractFloat at C:\Users\u009192\.julia\packages\COSMO\Sb5eV\src\i
nterface.jl:133
Stacktrace:
[1] load(optimizer::Optimizer{BigFloat}, a::MathOptInterface.VariablePrimalStart, vi::MathOptInterface.VariableIndex, value::Float64)
@ COSMO ~\.julia\packages\COSMO\Sb5eV\src\MOI_wrapper.jl:720
[2] load(model::Optimizer{BigFloat}, attr::MathOptInterface.VariablePrimalStart, indices::Vector{MathOptInterface.VariableIndex}, values::
Vector{Union{Nothing, Float64}})
@ MathOptInterface.Utilities ~\.julia\packages\MathOptInterface\1EYfq\src\Utilities\copy.jl:917
[3] _pass_attributes(dest::Optimizer{BigFloat}, src::MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.GenericModel{
Float64, MathOptInterface.Utilities.ModelFunctionConstraints{Float64}}}, idxmap::MathOptInterface.Utilities.IndexMap, attrs::Vector{MathOptI
nterface.AbstractVariableAttribute}, supports_args::Tuple{DataType}, get_args::Tuple{Vector{MathOptInterface.VariableIndex}}, set_args::Tupl
e{Vector{MathOptInterface.VariableIndex}}, pass_attr!::Function)
@ MathOptInterface.Utilities ~\.julia\packages\MathOptInterface\1EYfq\src\Utilities\copy.jl:300
[4] pass_attributes!(dest::Optimizer{BigFloat}, src::MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.GenericModel{
Float64, MathOptInterface.Utilities.ModelFunctionConstraints{Float64}}}, idxmap::MathOptInterface.Utilities.IndexMap, pass_attr::Function)
@ COSMO ~\.julia\packages\COSMO\Sb5eV\src\MOI_wrapper.jl:571
[5] pass_attributes!
@ ~\.julia\packages\COSMO\Sb5eV\src\MOI_wrapper.jl:559 [inlined]
[6] copy_to(dest::Optimizer{BigFloat}, src::MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.GenericModel{Float64,
MathOptInterface.Utilities.ModelFunctionConstraints{Float64}}}; copy_names::Bool)
@ COSMO ~\.julia\packages\COSMO\Sb5eV\src\MOI_wrapper.jl:148
[7] attach_optimizer(model::MathOptInterface.Utilities.CachingOptimizer{Optimizer{BigFloat}, MathOptInterface.Utilities.UniversalFallback{
MathOptInterface.Utilities.GenericModel{Float64, MathOptInterface.Utilities.ModelFunctionConstraints{Float64}}}})
@ MathOptInterface.Utilities ~\.julia\packages\MathOptInterface\1EYfq\src\Utilities\cachingoptimizer.jl:185
[8] optimize!(m::MathOptInterface.Utilities.CachingOptimizer{Optimizer{BigFloat}, MathOptInterface.Utilities.UniversalFallback{MathOptInte
rface.Utilities.GenericModel{Float64, MathOptInterface.Utilities.ModelFunctionConstraints{Float64}}}})
@ MathOptInterface.Utilities ~\.julia\packages\MathOptInterface\1EYfq\src\Utilities\cachingoptimizer.jl:248
[9] optimize!
@ ~\.julia\packages\MathOptInterface\1EYfq\src\Bridges\bridge_optimizer.jl:293 [inlined]
[10] solve!(problem::Problem{Float64}, optimizer::Optimizer{BigFloat}; check_vexity::Bool, verbose::Bool, warmstart::Bool, silent_solver::B
ool)
@ Convex ~\.julia\packages\Convex\O6nZN\src\solution.jl:243
[11] solve!(problem::Problem{Float64}, optimizer_factory::Function; kwargs::Base.Iterators.Pairs{Symbol, Bool, Tuple{Symbol}, NamedTuple{(:
warmstart,), Tuple{Bool}}})
@ Convex ~\.julia\packages\Convex\O6nZN\src\solution.jl:192
[12] top-level scope
@ REPL[662]:1
julia>
```

Looks like it’s trying to warm start with Float64s, although y contains BigFloat values. I’m guessing I need to set other things to BigFloats but I cant understand which ones.

Could someone guide me through it ?