Robust nonlinear optimization for R

When optim() fails on your ill-conditioned model, arcopt is designed to succeed. It uses Adaptive Regularization with Cubics (ARC) to handle indefinite Hessians and escape saddle points automatically.

Installation

# Install from GitHub
pak::pak("marcus-waldman/arcopt")
# Or with devtools
devtools::install_github("marcus-waldman/arcopt")

Quick Start

library(arcopt)
# Rosenbrock function - a classic difficult optimization problem
result <- arcopt(
  x0 = c(-1.2, 1),
  fn = function(x) (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2,
  gr = function(x) c(
    -2 * (1 - x[1]) - 400 * x[1] * (x[2] - x[1]^2),
    200 * (x[2] - x[1]^2)
  ),
  hess = function(x) matrix(c(
    1200 * x[1]^2 - 400 * x[2] + 2, -400 * x[1],
    -400 * x[1], 200
  ), 2, 2)
)
result$par
#> [1] 1 1

Two Modes: Exact Hessian vs Quasi-Newton

arcopt offers two optimization strategies:

Mode 1: Exact Hessian (Default)

Best when you can compute the Hessian analytically or via automatic differentiation.

# Provide fn, gr, and hess
result <- arcopt(x0, fn, gr, hess)

Mode 2: Quasi-Newton (No Hessian Required)

Best when computing the Hessian is expensive or unavailable. Uses BFGS/SR1 approximations. arcopt seeds the initial approximation