# JuMP, large expression, and hessian "limited-memory" option in Ipopt

**URL:** <https://discourse.julialang.org/t/jump-large-expression-and-hessian-limited-memory-option-in-ipopt/112609>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [April 6, 2024, 3:22pm UTC](https://discourse.julialang.org/t/jump-large-expression-and-hessian-limited-memory-option-in-ipopt/112609 "2024-04-06T15:22:28Z")\
**Posts on this page:** 1\
**Showing post:** 2

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [April 7, 2024, 10:32pm UTC](https://discourse.julialang.org/t/jump-large-expression-and-hessian-limited-memory-option-in-ipopt/112609/2 "2024-04-07T22:32:30Z")

</div>

Hi @niro, welcome to the forum!

> I was wondering if there a way to tell JuMP that I don’t want to compute the hessian information

To check if your settings make a difference, you can check the number of functions calls.

With:

```julia
using JuMP, Ipopt
function main(method)
    model = Model(Ipopt.Optimizer)
    @variable(model, x)
    @variable(model, y)
    @objective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)
    set_attribute(model, "hessian_approximation", method)
    optimize!(model)
end

```

I get

```julia
julia> main("exact")
This is Ipopt version 3.14.14, running with linear solver MUMPS 5.6.2.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 3

... lines omitted ...

Number of objective function evaluations = 36
Number of objective gradient evaluations = 15
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 14
Total seconds in IPOPT = 0.008

julia> main("limited-memory")
This is Ipopt version 3.14.14, running with linear solver MUMPS 5.6.2.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 0

... lines omitted ...

Number of objective function evaluations = 47
Number of objective gradient evaluations = 25
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 0
Total seconds in IPOPT = 0.043

```

The key difference is `Number of nonzeros in Lagrangian Hessian` and `Number of Lagrangian Hessian evaluations`, which are `0` if you set the limited-memory option. This shows that JuMP is not computing the Hessian, or passing it to Ipopt.

> Could it also speed up the line starting with @expression?

Nope

> does function tracing mean that AD is fully performed at this stage already

Nope.

> It works well but this step may take some time because the generated function may be quite lengthy.

For improving the speed of `@expression`, we can likely make some improvements. Can you provide a reproducible example of your code?

I really should write a tutorial on optimal control, with some common tricks for performance.

You could take a read of: [Help solving: Adding a few equations to ODE slows JuMP \>100x](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321)

Or look at

- [GitHub - control-toolbox/OptimalControl.jl: Solvers of optimal control problems](https://github.com/control-toolbox/OptimalControl.jl)
- [GitHub - JuliaControl/ModelPredictiveControl.jl: An open source model predictive control package for Julia.](https://github.com/JuliaControl/ModelPredictiveControl.jl)
- [GitHub - infiniteopt/InfiniteOpt.jl: An intuitive modeling interface for infinite-dimensional optimization problems.](https://github.com/infiniteopt/InfiniteOpt.jl)

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