Derivative-Based Optimization with User-Defined Convergence Criteria

Provides a derivative-based optimization framework that allows users to combine eight convergence criteria. Unlike standard optimization functions, this package includes a built-in mechanism to verify the positive definiteness of the Hessian matrix at the point of convergence. This additional check helps prevent the solver from falsely identifying non-optimal solutions, such as saddle points, as valid minima.

optimflex

optimflex provides a highly flexible suite of derivative-based non-linear optimization algorithms. It is specifically designed for researchers who require rigorous convergence control, particularly in complex models like SEM.

Why Use optimflex?

Standard optimization functions often rely on a single, fixed stopping rule. optimflex offers:

1. Strict Convergence Control: Choose from 8 distinct criteria.
2. The “AND” Rule: All selected criteria must be met simultaneously.
3. Hessian Verification: Verify local minima by checking positive definiteness at the final point.

Installation

# install.packages("devtools")
# devtools::install_github("yourusername/optimflex")

Basic Usage

library(optimflex)

rosenbrock <- function(x) {
  100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}

res <- double_dogleg(
  start = c(-1.2, 1.0),
  objective = rosenbrock,
  control = list(
    use_grad = TRUE,
    use_rel_x = TRUE,
    use_posdef = TRUE
  )
)

print(res$par)
#> [1] 0.9999955 0.9999910

Convergence Criteria Overview