RETRO.JL

REflective-bounds Trust-Region Optimizer

v0.0.1 · Julia

A high-performance, (nearly) allocation-free trust-region optimizer for bound-constrained nonlinear problems in Julia. Works with any AD backend via DifferentiationInterface.jl.

I want to:

Start optimizing

Install Retro, define a problem, and get a solution in five minutes.

→ Quick Start 02

Learn about the optimizer

A guided tour from gradient descent to a full trust-region reflective algorithm — concept by concept.

→ Algorithm Tutorial 03

Contribute

Dive into the API reference, architecture notes, and cache design to start extending Retro.

→ API Reference

A taste of Retro

using Retro, ForwardDiff

f(x) = 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2   # Rosenbrock

prob = RetroProblem(f, [-1.2, 1.0], AutoForwardDiff();
                    lb = [-5.0, -5.0], ub = [5.0, 5.0])

result = optimize(prob)

result.x            # ≈ [1.0, 1.0]
is_successful(result)  # true

Features at a glance

Feature	Details
Bound constraints	Coleman–Li reflective step with multiple reflections
Hessian strategies	BFGS (damped), SR1, Exact Hessian via AD
Subspace solvers	2-D eigenvalue, Steihaug–Toint CG, full-space
TR solvers	Eigenvalue, or Cauchy
AD backends	Any backend via DifferentiationInterface (ForwardDiff, Enzyme, …)
Zero-allocation loops	Pre-allocated `RetroCache` workspace
Display modes	`Silent()`, `Iteration()`, `Final()`, `Verbose()` (with ProgressMeter)

Acknowledgements

Retro.jl is heavily inspired by the fides optimizer in Python, as well as MATLAB's lsqnonlin optimizer.