Nonlinear expressions may contain only scalar

Specific Domains Optimization (Mathematical)
2

Welcome to JuMP!

Quite a few things:

  • You can use linear algebra (e.g., b' * e) in @constraint, but not @NLconstraint. It’s annoying, but we’re working on fixing it.
  • If the terms are linear or quadratic, you can use @constraint. You only need @NLconstraint for things other than linear and quadratic.
  • Your syntax for PSD constraints is slightly wrong
  • Ipopt doesn’t support PSD constraints

Here’s how I would re-write your constraints

using JuMP
s, e = 2, [1, 1]
model = Model()
@variable(model, a[1:s, 1:s] >= 0)
@variable(model, r[1:s, 1:s], Symmetric)
@variable(model, b[1:s] >= 0)

# You can use linear algebra in `@constraint`
@constraint(model, c1, b' * e == 1)
# but not in `@NLconstraint`
# @NLconstraint(model, c2, b' * c == 1/2)
# What is c???
# @NLconstraint(model, c2, sum(b[i] * c[i] for i in 1:s) == 1/2)

# @NLconstraint(model, c3, b' * (a*e).^2 == 1/3)
a_e = @expression(model, a * e)
@NLconstraint(model, c3, sum(b[i] * a_e[i]^2 for i in 1:s) == 1 / 3)

# @NLconstraint(model, c4, b' * a * (a*e) ==1/6)
a_a_e = @expression(model, a * a * e)
@NLconstraint(model, c4, sum(b[i] * a_a_e[i] for i in 1:s) == 1 / 6)

# @NLconstraint(model, c5, r*a + a'*r -b*b',PSD)
X = r * a + a' * r - b * b'
@constraint(model, c5, Symmetric(X) >= 0, PSDCone())

The c5 constraint is going to become a problem. I don’t know a solver which would support quadratic in PSD cone. and especially when it isn’t positive semidefinite.

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