Principle:Google deepmind Mujoco Newton Solver
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Optimization | 2025-02-15 |
Overview
Description: Newton's method applied to the constraint solving problem for faster quadratic convergence on smooth constraint formulations.
Context: MuJoCo's Newton solver is the default and generally recommended solver, providing robust convergence for the convex optimization problem that arises from MuJoCo's soft constraint model.
Theoretical Basis
The Newton solver minimizes a convex cost function over the constraint forces, using the Hessian (second derivative) to compute Newton steps. At each iteration, a linear system involving the Hessian is solved (using sparse Cholesky or similar factorization), and a line search ensures sufficient decrease in the cost. The soft constraint formulation in MuJoCo ensures that the Hessian is always positive definite, guaranteeing convergence. Newton's method achieves quadratic convergence near the solution, typically requiring fewer iterations than PGS for comparable accuracy.
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