我正在研究最小二乘问题，并尝试使用JuMP和Gurobi将给定的n点拟合为2条曲线。

此代码可用于创建一条曲线

using JuMP,Gurobi
m = Model(solver=GurobiSolver(Outputflag=0))
@variable( m,x[1:size(A,2)] )
@objective( m,Min,sum((A*x-b).^2) )
solve(m)

摘自这张幻灯片https://laurentlessard.com/teaching/cs524/slides/8%20-%20least%20squares.pdf

我的尝试在这里

# define (x,y) coordinates of the points
x = [ 1,2,3,4,5,6,7,8,9,2 ]
y = [ 1,1,4 ]

x1 = x[1:5]
x2 = x[5:9]

y1 = y[1:5]
y2 = y[5:9]
using pyplot
figure(figsize=(8,4))
plot(x,y,"r.",markersize=10)
axis([0,10,-2,8])
grid("on")

println(x1)
println(x2)
println(y1)
println(y2)

# order of polynomial to use
k = 3

# fit using a function of the form f(x) = u1 x^k + u2 x^(k-1) + ... + uk x + u{k+1}
n = length(x1)

A = zeros(n,k+1)
for i = 1:n
    for j = 1:k+1
        A[i,j] = x1[i]^(k+1-j)
    end
end

A1 = zeros(n,k+1)
for i = 1:n
    for j = 1:k+1
        A1[i,j] = x2[i]^(k+1-j)
    end
end

println(A)
print(A1)


# NOTE: must have either Gurobi or Mosek installed!

using JuMP,Gurobi

#m = Model(solver=MosekSolver(LOG=0))
m = Model(with_optimizer(Gurobi.Optimizer))
#m = Model(solver=GurobiSolver(Outputflag=1,NumericFocus=2))    # extra option to do extra numerical conditioning
#m = Model(solver=GurobiSolver(Outputflag=1,BarHomogeneous=1))  # extra option to use alternative algorithms

@variable(m,u[1:k+1])
@variable(m,v[1:k+1])
@variable(m,0 <= s[1:k+1] <= 1,integer=true)

@expression(m,su[i in 1:k+1],u'.*A[i,:])
@expression(m,sv[i in 1:k+1],v'.*A[i,:])

#@expression(model,q_expr[k=1:2],sum([sum([x[i]*x[j]*c[k] for i in 1:3]) for j in 1:3]))


@objective(m,sum( (1-s[i])*(y[i]-su[i]).^2 + s[i]*(y[i]-sv[i]).^2 for i in 1:k+1 ) )

optimize!(m)
uopt = value.(u)
println(uopt)

但是模型给出以下错误

Collection of expressions with @expression must be linear. For quadratic expressions,use your own array.

这无济于事https://discourse.julialang.org/t/collections-of-quadratic-expressions-causes-expression-to-throw-error/32359