# Matrix inverse in constraints in \`@NLconstraint\`
**URL:** https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462
**Category:** Optimization (Mathematical)
**Tags:** jump, optimization, nonlinear
**Created:** [October 9, 2022, 12:14am UTC](https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462 "2022-10-09T00:14:20Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Rick](https://discourse.julialang.org/u/Rick)
#### Post date: [October 9, 2022, 12:14am UTC](https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462/1 "2022-10-09T00:14:20Z")
Hi, I have a question related to nonlinear optimization.
I am trying to impose a nonlinear constraint that involves a matrix inversion. The matrix contains a variable of the optimization model. When I try to do this via `@NLconstraint`, I get an error. An example is as follows. May I know is there another way to properly impose these types of constraints, or should I use another optimizer? Many thanks!
```julia
using JuMP, NLopt
model = Model(NLopt.Optimizer)
set_optimizer_attribute(model, "algorithm", :LD_MMA)
@variable(model, x, lower_bound = 0)
@variable(model, y, lower_bound = 0)
M1 = [1 x; 0 1]
@NLconstraint(model, inv(M1) * [y; x] == [5; 1])
```
The error message that I get is:
```julia
LoadError: Unexpected array AffExpr[1 x; 0 1] in nonlinear expression. Nonlinear expressions may contain only scalar expressions.
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 9, 2022, 3:06am UTC](https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462/2 "2022-10-09T03:06:02Z")
The nonlinear syntax is limited: [Nonlinear Modeling · JuMP](https://jump.dev/JuMP.jl/stable/manual/nlp/#Scalar-operations-only). In particular, you can’t use vector-valued expressions.
If it’s just the linear solve you need, why do you need the explicit inverse? If I understand correctly, your model is equivalent to:
```julia
using JuMP
model = Model()
@variable(model, x >= 0)
@variable(model, y >= 0)
@constraint(model, [y, x] .== [1 x; 0 1] * [5, 1])
```
This is linear, with no need for an explicit matrix inverse.
---
### Author:  [@Rick](https://discourse.julialang.org/u/Rick)
#### Post date: [October 9, 2022, 3:15am UTC](https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462/3 "2022-10-09T03:15:05Z")
Thanks @odow.
The example here can be written as a linear form just for simplicity. What I was trying to do is related to a constraint that looks like A(x)B(x)^{-1}x = b, where A(x) and B(x) are two conformable matrices that contain the variable x.
Do you happen to know if there is another way to use vector-valued expressions, if it is not possible to be done in `JuMP`?
Thanks again!
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 9, 2022, 3:29am UTC](https://discourse.julialang.org/t/matrix-inverse-in-constraints-in-nlconstraint/88462/4 "2022-10-09T03:29:13Z")
> Do you happen to know if there is another way to use vector-valued expressions, if it is not possible to be done in `JuMP` ?
You can use vector-valued _linear_ or _quadratic_ expressions in the `@constraint` macro. You just can’t use vector-valued expressions in the `@NLxxx` macros.
I would split out the inner `inv(B(x)) * x` term:
```julia
using JuMP
model = Model()
@variable(model, x[1:2] >= 0)
A(x) = [1 x; 0 1]
B(x) = [1 x; 0 1]
b = [1, 2]
@variable(model, y[1:2])
@constraint(model, B(x) * y .== x)
@constraint(model, A(x) * y .== b)
```
Now you have two non-convex quadratic constraints.