gradient_descent
================

.. py:function:: t3toolbox.backend.optimizers.gradient_descent(problem, x0, n_iter = 100, gtol_rel = 1e-08, c_armijo = 0.0001)

   .. code-block:: python

      def gradient_descent(
              problem:  Problem,    # the fixed-rank least-squares problem
              x0:       Tangent,    # initial cores (U, G)
              n_iter:   int   = 100,
              gtol_rel: float = 1e-8,   # stop when ‖g‖ <= gtol_rel * ‖g_0‖
              c_armijo: float = 1e-4,   # Armijo sufficient-decrease constant
      ) -> typ.Tuple[Tangent, dict]:    # (x_cores, stats)


   Steepest descent with a Cauchy initial step and an **Armijo backtracking line search**. The step
   length starts at the Cauchy value ``α = ‖g‖² / ‖𝒥g‖²`` (the 1D minimizer of the local GN quadratic
   along ``−g``) and backtracks (``α ← α/2``) until ``f(retract(−α g)) ≤ f − c·α‖g‖²`` -- so it descends
   on any geometry, including the additive corewise chart where a bare Cauchy step overshoots the
   high-degree objective. Exercises the whole backend-first stack (``gradient`` / ``gn_quadratic`` /
   ``objective`` / ``retract``). (Eager; the jit kernel + the `xwhile` line search come in G3.3/G3.4.)