# How to code the following optimization problem
**URL:** https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098
**Category:** Optimization (Mathematical)
**Tags:** convex-optimization
**Created:** [October 2, 2021, 6:39am UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098 "2021-10-02T06:39:57Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Jaidy](https://discourse.julialang.org/u/Jaidy)
#### Post date: [October 2, 2021, 6:39am UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098/1 "2021-10-02T06:39:57Z")
Hi everyone,
I have the following optimization problem to solve:
minimize c^T_x, subject to ||c^T_x||\_1 \<= C
Can someone tell me how to write this in say NLopt, or any other library?
---
### Author:  [@zdenek\_hurak](https://discourse.julialang.org/u/zdenek_hurak)
#### Post date: [October 2, 2021, 2:03pm UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098/2 "2021-10-02T14:03:25Z")
The very problem statement is rather confusing. At least for me. I assume that `x` and `c` are vectors (1d arrays of numbers). Then `c^Tx` is a scalar, but what does `||c^Tx||_1` mean? Why wouldn’t the constraint be written just as `|c^Tx|<=C`?
If my understanding of the problem statement is correct, that is,
```nohighlight
minimize c'x
subject to |c'x|<=C
```
the solution is pretty straightforward, isn’t it? Minimization of a linear function(al) with a lower (and upper) bound on its value. For a nonzero `c`, the minimum value of the functional is `-C`. A minimizer `x` can be found by solving
`c'x = -C`.
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### Author:  [@Jaidy](https://discourse.julialang.org/u/Jaidy)
#### Post date: [October 2, 2021, 7:26pm UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098/3 "2021-10-02T19:26:03Z")
sorry, I wrote it wrong! The correct problem is
minimize 1’Ax,
subject to ||Ax||\_1 \<=C
here A is a matrix, 1 is a vector of all ones
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### Author:  [@zdenek\_hurak](https://discourse.julialang.org/u/zdenek_hurak)
#### Post date: [October 2, 2021, 10:04pm UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098/4 "2021-10-02T22:04:40Z")
```julia
using Convex, Clp
m,n = 2,3
A = rand(m,n)
γ = 3.0
x = Variable(n)
problem = minimize(sum(A*x), norm(A*x,1)<=γ)
solve!(problem, Clp.Optimizer)
problem.optval
x.value
```
---
### Author:  [@Jaidy](https://discourse.julialang.org/u/Jaidy)
#### Post date: [October 2, 2021, 10:57pm UTC](https://discourse.julialang.org/t/how-to-code-the-following-optimization-problem/69098/5 "2021-10-02T22:57:26Z")
thank you so much