Introduction

Apex Solver is a high-performance Rust library for nonlinear least squares optimization on Lie groups, aimed at SLAM, bundle adjustment and computer vision.

It bridges the gap between theoretical robotics and practical implementation:

• Manifold-aware optimization — full Lie group support (SO(2), SO(3), SE(2), SE(3), SE₂(3), SGal(3), Sim(3), ℝⁿ) with analytic Jacobians via the apex-manifolds crate.
• Three optimization algorithms — Levenberg–Marquardt (with Ceres-compatible Nielsen and Marquardt damping policies), Gauss–Newton and Dog Leg behind a unified Optimizer trait.
• Four sparse linear solvers — sparse Cholesky and QR, plus explicit and iterative (matrix-free PCG) Schur complement solvers for large-scale bundle adjustment.
• ~40 factors — pose, visual, IMU preintegration, LiDAR, GNSS, range and bearing, motion models and marginalization, each documented with its error and Jacobian in the Factor Reference.
• 15 robust loss functions — Huber, Cauchy, Tukey, Welsch, Barron and more, with correct Triggs correction of residuals and Jacobians.
• Zero-copy sparse linear algebra — parameters live in contiguous nalgebra storage viewed by faer without copying; unsafe is forbidden crate-wide.
• Ecosystem I/O — G2O, TORO and BAL file formats via the apex-io crate.
• Live visualization — integrated Rerun support for watching poses, landmarks, cost curves and sparsity patterns during a solve.

Where to go next

• Installation & Quick Start — solve your first pose graph.
• Problem Construction — variables, factors, keys and gauge freedom.
• Factor Reference — every factor’s error and Jacobian.
• Optimizers — choosing and tuning LM, GN and Dog Leg.
• Linear Solvers — Cholesky, QR and the Schur family.