Complementarity constraints containing sum statements

Specific Domains Optimization (Mathematical)
4

Not sure if this is the best way, but you can create an auxiliary expression with the sum and use the expression in complements:

using JuMP, Ipopt, Complementarity

m = Model(Ipopt.Optimizer)
@variable(m, x[i in 1:2]>=0)
@variable(m, l[j in 1:3])

@NLobjective(m, Min, (x[1] - 5)^2 + (2*x[2] + 1)^2)

@NLconstraint(m, 2*(x[2]-1) - 1.5*x[1] + l[1] - l[2]*0.5 + l[3] == 0)
@NLexpression(m,sumExp, sum(x[i] for i in 1:2)) #Create the expression


@complements(m, 0 <= 3*x[1] - x[2] - 3,        l[1] >= 0)
@complements(m, 0 <= - x[1] + 0.5*x[2] + 4,    l[2] >= 0)
@complements(m, 0 <= - x[1] - x[2] + 7,        l[3] >= 0)

@complements(m, 0 <= - sumExp + 7, l[3] >= 0) #Use the expression here

optimize!(m)
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