Add zero-iteration early exit to the primal solvers, certified by the duality gap.

The primal cost has curvature of at least M in every zone, making it strongly
convex in the M-norm and bounding the suboptimality of any point by the
Fenchel duality gap at its constraint forces:

  cost(qacc) - cost* <= 0.5*grad'*M^-1*grad

Since M's factorization always exists, this certificate is evaluable before
the solver does any work: one triangular solve and one dot product. When the
warmstarted solution is already certified to satisfy the tolerance, CG and
Newton now return with zero iterations; for Newton this skips building and
factorizing the Hessian. If the certificate declines, Newton gets a second
exit after factorization: the Newton decrement, checked before the first
line search.

Because the gap bounds cost suboptimality, stiff constraints can convert it
into force errors of order sqrt(2*gap*stiffness). Newton solutions are
characteristically force-accurate, so Newton zero-iteration exits also
require the gradient criterion, preserving constraint-force accuracy at
rest; CG solutions are characteristically cost-accurate and exit on the gap
alone.

On a settling pile of 50 boxes (300 dofs, ~200 contacts), end-to-end time
per step drops 13% over a settle-then-rest run and 27% in the quiescent
limit, with Newton iterations falling from 0.98 to 0.40 per step.

Tests: WarmstartZeroIterations sweeps solver/cone/jacobian on a settled box,
asserting zero iterations, forward/inverse consistency, and agreement with a
tolerance=0 control solve from the same state. WarmstartZeroIterationsIslands
checks per-island exits with a kicked box next to a settled one.
RefsiteConservesMomentum now requests an exact solve (tolerance=0), since it
asserts momentum conservation tighter than the solver tolerance contract.
PiperOrigin-RevId: 947993735
Change-Id: I2fd855774bff619709b2c386f1ba2714286e0821

doc/changelog.rst

@@ -13,6 +13,11 @@ General
   early-termination criterion of the :ref:`Newton solver<soAlgorithms>`, alongside cost improvement and gradient norm.
   This reduces iteration counts at no accuracy cost. Proposed by :github:user:`adenzler-nvidia` in
   :doc:`MJWarp <mjwarp/index>` pull request `1520 <https://github.com/google-deepmind/mujoco_warp/pull/1520>`__.
+- The CG and Newton solvers now terminate with zero iterations when a duality-gap certificate proves that the
+  warmstarted solution already satisfies the tolerance. The certificate requires only the existing mass-matrix
+  factorization, so quiescent scenes skip Hessian construction, factorization and the line search entirely. Newton
+  zero-iteration exits additionally require the gradient criterion, preserving Newton's characteristic force-level
+  accuracy. See :ref:`Warmstart<soAlgorithms>` in the Computation chapter for details.
 - :ref:`mj_encode` now supports encoding of MJB and TXT files.
 - :ref:`mj_setConst` now recomputes the ``mjModel.{body,geom,site}_sameframe`` flags, to account for changes in
   body/geom/site frames after compilation.