Warm-starting (set_start_value function) does not work in JuMP

Specific Domains Optimization (Mathematical)
1

Dear All,

I am trying to solve the following SDP with warm starting. The code is as follows

using JuMP, COSMO
    
# data
m = 5
n = 10
using Random: bitrand
c = randn(n)
x0 = bitrand(n)
A = randn(m, n)
b = A * x0 
x_prev = ones(n+1)
X_prev = x_prev*x_prev'

# JuMP model
    
sdp_model = JuMP.Model(COSMO.Optimizer)

@variables(sdp_model,
    begin
    X_tl[1 : n + 1, 1 : n + 1], PSD
end)

JuMP.set_start_value(X_tl, X_prev) 
# this line produces the following error:
# ERROR: MethodError: no method matching 
# set_start_value(::Symmetric{VariableRef,Array{VariableRef,2}}, ::Array{Float64,2})

obj = c' * X_tl[2:n + 1,1]

@objective(sdp_model, Min, obj)

@constraints(sdp_model, begin
    con_sdp_equality_1, A * X_tl[2:n + 1,1] .== b
    con_bound_1[i=1:n + 1, j=1:n + 1], X_tl[i,j] <= 1
    con_bound_2[i=1:n + 1, j=1:n + 1], X_tl[i,j] >= 0
end
    )

set_silent(sdp_model)

JuMP.optimize!(sdp_model)

obj_val = JuMP.objective_value(sdp_model)

X_sol = JuMP.value.(X_tl)

If I run the code I get the error

ERROR: MethodError: no method matching 
set_start_value(::Symmetric{VariableRef,Array{VariableRef,2}}, ::Array{Float64,2})

If I comment the line JuMP.set_start_value(...,...) , then the code runs without any problem. I have tried the code with other solvers such as Mosek etc, but it is the same error.

Any help or suggestions will be much appreciated!

Best Regards,
Shuvo

2

Try broadcasting it with JuMP.set_start_value.(X_tl, X_prev) (note the added . at the end of the function name to broadcast the call to every element).

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3

Yes, that solved it, thank you so much!

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