JuMP Non-Linear Optimization

Here you go:

using JuMP, Ipopt
model = Model(Ipopt.Optimizer)
@variable(model, 0 <= x[1:2] <= 1)
@constraint(model, sum(x) == 1)
A = [0.00076204 0.00051972; 0.00051972 0.00546173]
@expression(model, quad_expr, x' * A * x)
@NLobjective(model, Min, sqrt(quad_expr))
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