Fix/simplify tutorial.

tutorials/StochasticGradientDescent.qmd

@@ -95,32 +95,32 @@ p_opt2 = stochastic_gradient_descent(M, gradf, p0)
 
 This result is reasonably close. But we can improve it by using a `DirectionUpdateRule`, namely:
 
-On the one hand [`MomentumGradient`](https://manoptjl.org/stable/solvers/gradient_descent.html#Manopt.MomentumGradient), which requires both the manifold and the initial value, to keep track of the iterate and parallel transport the last direction to the current iterate.
+On the one hand [`MomentumGradient`](@ref), which requires both the manifold and the initial value, to keep track of the iterate and parallel transport the last direction to the current iterate.
 The necessary `vector_transport_method` keyword is set to a suitable default on every manifold,
 see ``[`default_vector_transport_method`](@extref `ManifoldsBase.default_vector_transport_method-Tuple{AbstractManifold}`)``{=commonmark}. We get
 """
 
 ```{julia}
 p_opt3 = stochastic_gradient_descent(
-    M, gradf, p0; direction=MomentumGradient(M, p0; direction=StochasticGradient(M))
+    M, gradf, p0; direction=MomentumGradient(; direction=StochasticGradient())
 )
 ```
 
 ```{julia}
-MG = MomentumGradient(M, p0; direction=StochasticGradient(M));
-@benchmark stochastic_gradient_descent($M, $gradf, $p0; direction=$MG)
+MG = MomentumGradient(; direction=StochasticGradient());
+@benchmark stochastic_gradient_descent($M, $gradf, p=$p0; direction=$MG)
 ```
 
 And on the other hand the [`AverageGradient`](https://manoptjl.org/stable/solvers/gradient_descent.html#Manopt.AverageGradient) computes an average of the last `n` gradients. This is done by
 
 ```{julia}
 p_opt4 = stochastic_gradient_descent(
-    M, gradf, p0; direction=AverageGradient(M, p0; n=10, direction=StochasticGradient(M)), debug=[],
+    M, gradf, p0; direction=AverageGradient(; n=10, direction=StochasticGradient()), debug=[],
 )
 ```
 ```{julia}
-AG = AverageGradient(M, p0; n=10, direction=StochasticGradient(M));
-@benchmark stochastic_gradient_descent($M, $gradf, $p0; direction=$AG, debug=[])
+AG = AverageGradient(; n=10, direction=StochasticGradient(M));
+@benchmark stochastic_gradient_descent($M, $gradf, p=$p0; direction=$AG, debug=[])
 ```
 
 Note that the default `StoppingCriterion` is a fixed number of iterations which helps the comparison here.