Optex - mathematical optimization (LP/MILP/QP/SOCP) with in-process solvers

I’ve released Optex, a library for modeling and solving mathematical optimization problems from Elixir, with the solvers running in-process via Rustler rather than behind a service call.

If you’ve ever needed to answer “what’s the cheapest way to do this given these constraints”: scheduling shifts, routing deliveries, allocating inventory, picking which warehouses to open, that’s a linear or mixed-integer program, and the answer until now was to stand up a Python service with PuLP or gurobipy and talk to it over HTTP. Optex removes that boundary.

It works in Livebook with no toolchain:

Mix.install([{:optex, "~> 0.1.1"}])

HiGHS ships precompiled for x86_64/aarch64 Linux, x86_64/aarch64 macOS, and x86_64 Windows, so that’s a checksummed binary download and you’re solving MILPs in a notebook. No Rust, no CMake.

What a model looks like:

import Optex.DSL

m =
  model sense: :max do
    variable take[i], i <- items, type: :bin
    constraint sum(weight[i] * take[i], i <- items) <= capacity
    objective sum(value[i] * take[i], i <- items)
  end

{:ok, sol} = Optex.optimize(m)
sol.objective       #=> optimal value
sol.values[{:take, 3}]

The DSL is macro-based, so it reads your expressions structurally at compile time. Trailing generators declare families (one row per binding) and options are evaluated per binding with the generators in scope, so bounds and types can depend on the index.

Where the BEAM actually earns its keep:

Models are immutable values. There’s no solver handle to guard, no environment to pool, so a scenario study is just data work:

scenarios
|> Task.async_stream(&Optex.optimize(build_model(&1)))
|> Enum.to_list()

Solves run on dirty schedulers, so a long branch-and-bound doesn’t stall your schedulers. And instead of C callbacks, progress and improving solutions arrive as ordinary messages:

Optex.optimize(m, progress: self(), incumbents: self())
# {:optex_progress, %{best_obj: _, best_bound: _, gap: _, nodes: _}}
# {:optex_incumbent, %{objective: _, values: _}}

Combine that with a cancel token and a stopping rule is a receive loop in your own process. It’s the same code on every backend, it can’t crash the solver, and it drops straight into a LiveView if you want a progress bar on a running solve.

Scope: LP, MILP, QP, QCP, SOCP. Native indicator constraints, absolute values, piecewise-linear functions, min/max, and SOS on backends that support them. Duals and reduced costs for LPs, IIS-based infeasibility diagnosis, LP/MPS export. HiGHS is built in; Gurobi, CPLEX, and COPT compile if you have them installed and licensed.

One opinionated bit: if you ask for something your chosen solver doesn’t natively support, it fails before solving rather than quietly rewriting your model into a big-M formulation. JuMP will bridge those automatically; Optex refuses on purpose, because a silent rewrite needs bounds you may not have given and can wreck solve times in ways that surface as a production mystery instead of an error. The examples show the manual reformulations side by side with the native constructs so you can pick with both costs visible.

There are 23 runnable examples in the repo and a Livebook tour. Longer design rationale in docs/design_notes.md, and there’s an Elixir primer aimed at people arriving from JuMP or gurobipy.

It’s v0.1.1 and I’d genuinely like to hear from anyone who puts it near a real problem. The biggest known gap is persistent solver handles and warm starts for re-solve loops, I’ve deliberately not designed that yet because I’d rather build it against someone’s actual mutation patterns than guess.