Module optimizers 

Optimizers for solving non-linear least squares problems.

Specifically, given a nonlinear least squares problem of the form,

$$ \Theta^* = \argmin_{\Theta} \sum_{i} \rho_i(||r_i(\Theta)||_{\Sigma_i} ) $$

These optimizers function by first, linearizing to a linear least squares problem, $$ \Delta \Theta = \argmin_{\Delta \Theta} \sum_{i} ||A_i (\Delta \Theta)_i - b_i ||^2 $$

This can be rearranged to a large, sparse linear system given by,

$$ A \Delta \Theta = b $$

which can then be solved. For example, Gauss-Newton solves this directly, while Levenberg-Marquardt adds a damping term to the diagonal of $A^\top A$ to ensure positive definiteness.

This module provides a set of optimizers that can be used to solve non-linear least squares problems. Each optimizer implements the Optimizer trait to give similar structure and usage.

Additionally observers can be added to the optimizer to monitor the progress of the optimization. A prebuilt Rerun can be enabled via the rerun feature.

If you desire to implement your own optimizer, we additionally recommend using the test_optimizer macro to run a handful of simple tests over a few different variable types to ensure correctness.

Structs

GaussNewton

The Gauss-Newton optimizer

LevenMarquardt

The Levenberg-Marquadt optimizer

OptObserverVec

Observer collection for optimization

OptParams

Parameters for the optimizer

Enums

OptError

Error types for optimizers

Traits

OptObserver

Observer trait for optimization

Optimizer

Trait for optimization algorithms

Type Aliases

OptResult

Result type for optimizers