Hello,

I’m minimizing the analitic center of a set of inequalities (see problem 9.30 Convex Optimization Boyd and Vandenberghe).

I generate a random instance as follows:

```
n=8
m=7
A=rand(m,n)
```

Then I create the necessary functions:

```
f(x) = - 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
```

If I optimize f(x), without using the information of the gradient and hessian I get:

```
res = optimize(f, zeros(n), NelderMead())
Results of Optimization Algorithm
* Algorithm: Nelder-Mead
* Starting Point: [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
* Minimizer: [-0.45985687074938164,-0.4699442909210658, ...]
* Minimum: -5.254794e+00
* Iterations: 374
* Convergence: true
* √(Σ(yᵢ-ȳ)²)/n < 1.0e-08: true
* Reached Maximum Number of Iterations: false
* Objective Calls: 639
```

However, if I try to use this information (GradientDescent()-Newton(),NewtonTrustRegion()):

```
optimize(f, ∇f!, zeros(n), GradientDescent())
ArgumentError: Value and slope at step length = 0 must be finite.
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:116
```

```
optimize(f, ∇f!, Δf!, zeros(n), Newton())
DomainError()
in optimize at Optim/src/multivariate/optimize/interface.jl:126
in optimize at Optim/src/multivariate/optimize/optimize.jl:49
in update_state! at Optim/src/multivariate/solvers/second_order/newton.jl:83
in perform_linesearch! at Optim/src/utilities/perform_linesearch.jl:40
in at LineSearches/src/hagerzhang.jl:101
in at LineSearches/src/hagerzhang.jl:215
in at LineSearches/src/LineSearches.jl:87
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:144
in mapfoldl at base/reduce.jl:71
in at base/<missing>
in log at base/math.jl:419
in nan_dom_err at base/math.jl:300
```

```
optimize(f, ∇f!, Δf!, zeros(n), NewtonTrustRegion())
BoundsError: attempt to access 0-element Array{Float64,1} at index [1]
in optimize at Optim/src/multivariate/optimize/interface.jl:126
in optimize at Optim/src/multivariate/optimize/optimize.jl:49
in update_state! at Optim/src/multivariate/solvers/second_order/newton_trust_region.jl:266
in #solve_tr_subproblem!#60 at Optim/src/multivariate/solvers/second_order/newton_trust_region.jl:85
in getindex at base/array.jl:554
```

I’m not sure if the source of the error is evident.

Thank you!