Add the Newton decrement as a termination criterion of the Newton solver.
After an accepted line-search step, the solver has already rebuilt the gradient and Hessian and solved for the next search direction, so the Newton decrement 0.5*g'*H^-1*g -- the quadratic model's predicted cost improvement of the next iteration -- costs one dot product. Terminating when it falls below tolerance avoids running one more iteration only to observe a correspondingly small actual improvement. This is a C port of Alain's proposal in MJWarp: https://github.com/google-deepmind/mujoco_warp/pull/1520 PiperOrigin-RevId: 947768034 Change-Id: I94e5c71a4e2b4a7775611edd1dad254bba2633b4
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@@ -1392,7 +1392,10 @@ representations of the constraint Jacobian and related matrices.
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This algorithm implements the exact Newton method, with analytical second-order derivatives and Cholesky
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factorization of the Hessian. The line-search is the same as in the CG method. When constraint states change between
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iterations (e.g., a constraint transitions from quadratic to linear), the Hessian factorization is updated
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incrementally via rank-1 Cholesky updates, avoiding full refactorization. It is the default solver.
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incrementally via rank-1 Cholesky updates, avoiding full refactorization. Early termination is triggered when any of
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three quantities falls below :ref:`tolerance<option-tolerance>`: the cost improvement of the last iteration, the
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gradient norm, and the Newton decrement :math:`\tfrac{1}{2} g^T H^{-1} g` -- the predicted cost improvement of the
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next iteration. It is the default solver.
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**PGS** : Projected Gauss-Seidel method
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This is the most common algorithm used in physics simulators, and used to be the default in MuJoCo, until we
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