# NLopt optimization with inequality constraint where objective function is undefined outside of the constraint
**URL:** https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924
**Category:** General Usage
**Tags:** optimization
**Created:** [April 8, 2019, 3:23pm UTC](https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924 "2019-04-08T15:23:57Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Shunsuke-Hori](https://discourse.julialang.org/u/Shunsuke-Hori)
#### Post date: [April 8, 2019, 3:23pm UTC](https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924/1 "2019-04-08T15:23:57Z")
Hello,
I would like to do nonlinear optimization with inequality constraint by `NLopt`, in which my objective function is not defined when the constraint is not satisfied. I’m using `LN_COBYLA` because I cannot compute the derivative.
However, the solver sometimes try to evaluate the objective function outside of the constraint and, as a consequence, the solver fails.
The minimal example below shows the problem.
I know I can impose a bounds constraint for this simple example but not in general.
Is there any way to search values only inside of the constraint? (What I can come up with is to let the objective function return huge value when undefined, although I don’t think it’s a beautiful solution.)
Thank you.
=======================
Example: \min x\_1+x\_2 subject to x\_1\geq0 and x\_2\geq0 but x\_1+x\_2 is undefined for x\_1\<0 or x\_2\<0
```julia
using NLopt
function obj(x, grad)
if any(x .<0)
println("negative element")
println(x)
return error("undefined")
else
return x[1]+x[2]
end
end
function myconstraint(result, x, grad)
result .= -x
end
opt = Opt(:LN_COBYLA, 2)
min_objective!(opt, obj)
inequality_constraint!(opt, myconstraint, [0, 0])
optimize(opt, [0.001, 0.001])
```
return
```julia
undefined
[-0.000320083, 0.000507602]
(0.000585786437626905, [0.000292893, 0.000292893], :FORCED_STOP)
```
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [April 8, 2019, 4:05pm UTC](https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924/2 "2019-04-08T16:05:31Z")
Do a domain transformation, such as using `x^2` or `exp(x)` as the input, so that way it is defined on the full real lined.
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [April 9, 2019, 1:33am UTC](https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924/3 "2019-04-09T01:33:27Z")
> [@Shunsuke-Hori](#):
>
> I would like to do nonlinear optimization with inequality constraint by `NLopt` , in which my objective function is not defined when the constraint is not satisfied. I’m using `LN_COBYLA` because I cannot compute the derivative.
> However, the solver sometimes try to evaluate the objective function outside of the constraint and, as a consequence, the solver fails.
For _general nonlinear constraints_, NLopt makes no guarantee that it will only evaluate points inside the feasible set (i.e. satisfying the constraints).
However, for a constraint like x₁ ≥ 0, you should instead specify the constraint as a bound constraint via `opt.lower_bounds = ...` Not only is this much more efficient, but also NLopt guarantees that it will never evaluate a point outside of the bound constraints.
---
### Author:  [@Shunsuke-Hori](https://discourse.julialang.org/u/Shunsuke-Hori)
#### Post date: [April 10, 2019, 1:43am UTC](https://discourse.julialang.org/t/nlopt-optimization-with-inequality-constraint-where-objective-function-is-undefined-outside-of-the-constraint/22924/4 "2019-04-10T01:43:23Z")
Thank you both,
It’s good to know there is no way to force the solver to use a value satisfying the constraint.
I’ll think about change of variables so that I can use box constraints, although I’m not sure if I can.