# How to add this formula as an objective function?
**URL:** https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345
**Category:** Optimization (Mathematical)
**Tags:** question
**Created:** [October 1, 2019, 1:33am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345 "2019-10-01T01:33:18Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Shor](https://discourse.julialang.org/u/Shor)
#### Post date: [October 1, 2019, 1:33am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/1 "2019-10-01T01:33:18Z")
Hi, I am new here.
I don’t know how to add this formula in my minimization objective function.
where //x//\_1 stands for the sum of the absolute values of the components of x. (x is a 10x1 array)
Anyone can help me with this?
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### Author:  [@longemen3000](https://discourse.julialang.org/u/longemen3000)
#### Post date: [October 1, 2019, 5:16am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/2 "2019-10-01T05:16:16Z")
maybe `sum(abs.(x))` ? the dot means that the function is applied over all elements of the array (is called broadcasting)
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### Author:  [@Azamat](https://discourse.julialang.org/u/Azamat)
#### Post date: [October 1, 2019, 5:50am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/3 "2019-10-01T05:50:37Z")
You can handle this problem by lifting it’s formulation, i.e. introducing new dummy decision variable t, adding constraints \quad x ≤ t; \quad -x ≤ t and then modifying the objective function as \lVert Ax - b\rVert\_2 + λt. With this formulation we reduced the problem to the classical constrained quadratic program, which can be handled easily with JuMP (check it’s documentation)
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### Author:  [@ericphanson](https://discourse.julialang.org/u/ericphanson)
#### Post date: [October 1, 2019, 6:45am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/4 "2019-10-01T06:45:44Z")
I don’t think that works if `x` is a vector (your inequalities interpreted point wise give the infinity norm, not the one norm).
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### Author:  [@Azamat](https://discourse.julialang.org/u/Azamat)
#### Post date: [October 1, 2019, 7:46am UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/5 "2019-10-01T07:46:43Z")
Yes, you are right. This should work:
\min ∥ A x − b ∥\_2 + λ \sum\_{i=1}^{n} t\_i;\quad x \preccurlyeq t ;\quad − x \preccurlyeq t
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### Author:  [@Shor](https://discourse.julialang.org/u/Shor)
#### Post date: [October 1, 2019, 3:21pm UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/6 "2019-10-01T15:21:33Z")
Yes. I tried this code but Julia returns this error: MethodError: no method matching abs(::Array{VariableRef,1})
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### Author:  [@Shor](https://discourse.julialang.org/u/Shor)
#### Post date: [October 1, 2019, 4:15pm UTC](https://discourse.julialang.org/t/how-to-add-this-formula-as-an-objective-function/29345/7 "2019-10-01T16:15:51Z")
It works. Thank you!