使用nlme包gnls函数时，nlminb的PORT routines包含哪些优化算法？

Hey there! Let me clarify this for you since it's a common point of confusion when working with nlme and optimization in R.

First off: PORT routines are a collection of numerical optimization algorithms, not a single standalone algorithm. They originate from the PORT library developed at Bell Labs, a classic toolkit for solving various optimization problems efficiently. R's nlminb() function leverages this library for both unconstrained and box-constrained minimization tasks, which is why you ended up here when digging into gnls()'s optimizer.

Key Algorithms Included in PORT Routines #

Let's break down the main types you'll encounter:

• Quasi-Newton methods (for unconstrained optimization): The core workhorses here are algorithms like BFGS and DFP. These methods approximate the second-order Hessian matrix (without computing it directly) to speed up convergence—way more efficient than basic gradient descent, which only uses first-order information. nlminb() will default to these unless you specify otherwise, and they handle most smooth unconstrained minimization tasks really well.
• Box-constrained optimization variants: PORT has adapted its quasi-Newton methods to handle variables with upper/lower bounds (box constraints). It uses techniques like variable transformation or projection to keep parameters within their allowed ranges while maintaining the efficiency of the underlying quasi-Newton logic.

Comparing to the Algorithms You Mentioned #

• Gradient Descent: Basic gradient descent isn't part of the PORT routines. The quasi-Newton methods in PORT are far more efficient for most practical problems, as they adapt their step size based on approximated curvature information, rather than using a fixed or slowly adapting step like vanilla gradient descent.
• Levenberg–Marquardt: This is a specialized algorithm for nonlinear least squares problems (which is exactly what gnls() is solving!). While gnls() can use Levenberg–Marquardt in some cases (via the control arguments), when it falls back to nlminb(), it's using PORT's quasi-Newton methods instead. Levenberg–Marquardt is tailored specifically for sum-of-squares objectives, whereas PORT's routines are general-purpose minimizers that work for any smooth objective function.

Quick Note for Your gnls() Workflow #

If you want to confirm which optimizer gnls() is using, you can check the control argument—gnlsControl() lets you specify optimizers, including switching between nlminb() (PORT) and Levenberg–Marquardt directly.

内容的提问来源于stack exchange，提问作者noobie2023