### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [June 19, 2018, 12:30am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/2 "2018-06-19T00:30:12Z")
I get a negative log when running your code? Also your gradient is wrong:
```julia
function ∇f!(g, x)
g = sum(A[i,:]/(1-dot(A[i,:],x)) for i=1:m) + 2*x./(1-x.^2)
end
```
does not do what you think it does but creates a new variable g which shadows the old one. Use `.=` or `copy!`. @pkofod possibly we could have a clearer error message here?
---
### Author:  [@tlagos](https://discourse.julialang.org/u/tlagos)
#### Post date: [June 19, 2018, 1:13am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/3 "2018-06-19T01:13:03Z")
Great!
Now NewtonTrustRegion() works:
```julia
Results of Optimization Algorithm
* Algorithm: Newton's Method (Trust Region)
* Starting Point: [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
* Minimizer: [-0.4642088906377006,-0.5205478310783768, ...]
* Minimum: -5.958903e+00
* Iterations: 11
* Convergence: true
* |x - x'| ≤ 0.0e+00: false
|x - x'| = 1.34e-08
* |f(x) - f(x')| ≤ 0.0e+00 |f(x)|: false
|f(x) - f(x')| = -2.98e-16 |f(x)|
* |g(x)| ≤ 1.0e-08: true
|g(x)| = 8.97e-09
* Stopped by an increasing objective: false
* Reached Maximum Number of Iterations: false
* Objective Calls: 12
* Gradient Calls: 12
* Hessian Calls: 11
```
It seems you are right about the negative result inside the logarithm. So I have changed f(x) to its extended domain function:
```julia
f(x) = any(A*x.>=1) ? Inf : ( - sum(log(1-dot(A[i,:],x)) for i=1:m) - sum(log(1 - x[i]^2.) for i=1:n))
function ∇f!(g, x)
g .= sum(A[i,:]/(1-dot(A[i,:],x)) for i=1:m) + 2*x./(1-x.^2)
end
function Δf!(h, x)
h .= sum(A[i,:]*transpose(A[i,:]) / (1-dot(A[i,:],x))^2 for i=1:m) +
diagm( (2 + 2*x.^4) ./ (1-x.^2).^2)
end
```
Now both GradientDescent() and Newton() are having the same error.
```julia
DomainError()
in optimize at Optim/src/multivariate/optimize/interface.jl:119
in #optimize#132 at Optim/src/multivariate/optimize/interface.jl:121
in optimize at Optim/src/multivariate/optimize/optimize.jl:49
in update_state! at Optim/src/multivariate/solvers/first_order/gradient_descent.jl:74
in perform_linesearch! at Optim/src/utilities/perform_linesearch.jl:40
in at LineSearches/src/hagerzhang.jl:101
in at LineSearches/src/hagerzhang.jl:136
in at LineSearches/src/LineSearches.jl:87
in value_gradient! at Optim/src/Manifolds.jl:47
in value_gradient! at NLSolversBase/src/interface.jl:75
in value_gradient!! at NLSolversBase/src/interface.jl:88
in at NLSolversBase/src/objective_types/abstract.jl:14
in f at example_convex.jl:145
in mapfoldl at base/reduce.jl:71
in at base/
in log at base/math.jl:419
in nan_dom_err at base/math.jl:300
```
---
### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [June 19, 2018, 1:31am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/4 "2018-06-19T01:31:01Z")
These solvers are not designed to handle functions that have infinities. Fix your initialization to get a feasible point.
---
### Author:  [@tlagos](https://discourse.julialang.org/u/tlagos)
#### Post date: [June 19, 2018, 1:50am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/5 "2018-06-19T01:50:03Z")
Yes, x0=zeros(n), is always a feasible start point:
```julia
( - sum(log(1-dot(A[i,:],x)) for i=1:m) - sum(log(1 - x[i]^2.) for i=1:n)) = 0
```
Still it throws the same error.
---
### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [June 19, 2018, 2:03am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/6 "2018-06-19T02:03:54Z")
You’re missing one part: `f(x) = (any(A*x.>=1) || any(abs(x) .>= 1)) ? Inf : ( - sum(log(1-dot(A[i,:],x)) for i=1:m) - sum(log(1 - x[i]^2.) for i=1:n))` works.
---
### Author:  [@tlagos](https://discourse.julialang.org/u/tlagos)
#### Post date: [June 19, 2018, 2:20am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/7 "2018-06-19T02:20:19Z")
> [@antoine-levitt](#):
>
> `(any(A*x.>=1) || any(abs(x) .>= 1)) ? Inf : ( - sum(log(1-dot(A[i,:],x)) for i=1:m) - sum(log(1 - x[i]^2.) for i=1:n))`
Thank you very much! It work perfectly!
---
### Author:  [@pkofod](https://discourse.julialang.org/u/pkofod)
#### Post date: [June 19, 2018, 9:10am UTC](https://discourse.julialang.org/t/optim-jl-argumenterror-value-and-slope-at-step-length-0-must-be-finite/11770/8 "2018-06-19T09:10:24Z")
Yes, the line search could / should inform the users of the likely reasons instead of just stating that something is zero 🙂