# Linearization
**URL:** https://discourse.julialang.org/t/linearization/58167
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [March 29, 2021, 3:31pm UTC](https://discourse.julialang.org/t/linearization/58167 "2021-03-29T15:31:37Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@user1200](https://discourse.julialang.org/u/user1200)
#### Post date: [March 29, 2021, 3:31pm UTC](https://discourse.julialang.org/t/linearization/58167/1 "2021-03-29T15:31:37Z")
Hi
I have simple objective function (goal), solving with Ipopt
for example:
`Min, sum (sin(data[i]*x) for i=1:length(data) )`
I was just curious if there is some way/wrap to achieve :
maximize linearity of **process** to goal.
Like in this example obj is Min, sum - so process is simple cumsum.
_Reason behind this is to work with trajectory (process), for example finding path which looks (the most) like “line”._
I tried like “distance between process’s segments”, but it doesnt seem to work in Ipopt.
(I found some math hints but too math 😊
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [March 29, 2021, 8:32pm UTC](https://discourse.julialang.org/t/linearization/58167/2 "2021-03-29T20:32:16Z")
Hi there.
> I tried like “distance between process’s segments”
Take a read of [Please read: make it easier to help you](https://discourse.julialang.org/t/psa-make-it-easier-to-help-you/14757). It’s easier to help if you can provide the code as a minimal working example.
> maximize linearity of **process** to goal
Can you clarify what this means?
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### Author:  [@user1200](https://discourse.julialang.org/u/user1200)
#### Post date: [March 30, 2021, 10:44am UTC](https://discourse.julialang.org/t/linearization/58167/3 "2021-03-30T10:44:25Z")
Hi
Thanks, yes:
Code is
```julia
using Random
using JuMP
using Ipopt
Random.seed!(1234)
n=1000
data = randn(n)
model = Model(Ipopt.Optimizer)
@variable(model, x)
@variable(model, a) #max distance
@NLexpressions(model, begin
y[ii=1:10], sum( sin(x*data[i]) for i = 1+floor(Int,(n/10)*ii-1):floor(Int,(n/10)*ii) ) # 10 segments y[1:10] - just cumsum
yy[ii=1:9], (-y[ii]+y[ii+1] )^2 # just abs(distance) , but ^2
end)
@NLconstraint(model, [i=1:9],yy[i] <= a) #max distance , 10 segments=9 distances
#@NLconstraint(model, [i=1:9],yy[i] >= 2) #next to implement : slope of process, each segment must raise minimum 2)
@NLobjective(
model,
Min,
a # minimize max distance
)
optimize!(model)
print( objective_value(model) )
value.(y) # currently zeros(10), but when slope added
```
**Usage:**
Normaly I just min/max objective function, but in graph ( **y** here) I observe sometimes very strange behaviours. So if graph of process looks like line, it would be very good.
**Example:**
I have other max objective function working with Ipopt. Sometimes value of y[i] jumps above global optimum, then went down.
From time perspective (y[1]…y[10]), I was curious, if there is (simplyfied 🥦 ) way to ‘model’ graph.
Image:
(1) Current situation, ignoring graph, only min/max obj (newest y[10]
(2) Better graph
\*(3) Line graph
\*(4) Best line graph with high obj
_( \* good solutions)_
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [March 30, 2021, 10:09pm UTC](https://discourse.julialang.org/t/linearization/58167/4 "2021-03-30T22:09:33Z")
I still don’t really understand the problem I’m afraid. You’re picking `x` that minimizes the maximum distance between two points `y[i]`?
Ipopt assumes the problem is convex, so using a function like `sin` will result in a locally optimal solution. You may see some weird artifacts. You could try multiple restarts by using `@variable(model, x, start = 1.0)` for different `start` values.