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/XMLreference.rst

@@ -418,9 +418,10 @@ adjust it properly through the XML.
 
 :at:`iterations`: :at-val:`int, "100"`
    Maximum number of iterations of the constraint solver. When the warmstart attribute of :ref:`flag <option-flag>` is
-   enabled (which is the default), accurate results are obtained with fewer iterations. Larger and more complex systems
-   with many interacting constraints require more iterations. Note that mjData.solver contains statistics about solver
-   convergence, also shown in the profiler.
+   enabled (which is the default), accurate results are obtained with fewer iterations; if the warmstarted solution
+   already satisfies the tolerance, the CG and Newton solvers terminate with zero iterations. Larger and more complex
+   systems with many interacting constraints require more iterations. Note that mjData.solver contains statistics about
+   solver convergence, also shown in the profiler.
 
 .. _option-tolerance:
 
@@ -428,7 +429,9 @@ adjust it properly through the XML.
    Tolerance threshold used for early termination of the iterative solver. For PGS, the threshold is applied to the cost
    improvement between two iterations. For CG and Newton, it is applied to the smaller of the cost improvement and the
    gradient norm. For Newton, it is additionally applied to the Newton decrement :math:`\tfrac{1}{2} g^T H^{-1} g`, the
-   predicted cost improvement of the next iteration. Set the tolerance to 0 to disable early termination.
+   predicted cost improvement of the next iteration. Before the first iteration, CG and Newton also apply it to a
+   :ref:`convergence certificate<soAlgorithms>` of the warmstarted solution, possibly terminating with zero iterations.
+   Set the tolerance to 0 to disable early termination.
 
 .. _option-ls_iterations: