Update tutorial.rst

Author: leclere

doc/tutorial.rst

@@ -12,10 +12,11 @@ Work with PolyhedralFunction
 
 Get Bellman value at a given point
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-We could estimate the Bellman value at a given position :code:`xt` with a :code:`PolyhedralFunction` :code:`Vt` ::
+To estimate the Bellman value at a given position :code:`xt` with a :code:`PolyhedralFunction` :code:`Vt` ::
 
     vx = get_bellman_value(model, param, t, Vt, xt)
-
+    
+This is a lower bound of the true value.
 
 Get optimal control at a given point
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -24,20 +25,20 @@ To get optimal control at a given point :code:`xt` and for a given alea :code:`x
 
     get_control(model, param, lpproblem, t, xt, xi)
 
-where :code:`lpproblem` is the linear problem storing evaluation of Bellman function at time :math:`t`.
+where :code:`lpproblem` is the linear problem storing the evaluation of Bellman function at time :math:`t`.
 
 
 
 Save and load pre-computed cuts
 ===============================
 
-We suppose that we have computed Bellman functions with SDDP. These functions are stored in a vector of :code:`PolyhedralFunctions` denoted :code:`V`
+Assume that we have computed Bellman functions with SDDP. These functions are stored in a vector of :code:`PolyhedralFunctions` denoted :code:`V`
 
-These functions could be stored in a text file with the command::
+These functions can be stored in a text file with the command::
 
     StochDynamicProgramming.dump_polyhedral_functions("yourfile.dat", V)
 
-And we could load them with the function::
+And then be loaded with the function::
 
     Vdump = StochDynamicProgramming.read_polyhedral_functions("yourfile.dat")
 
@@ -46,15 +47,15 @@ And we could load them with the function::
 Build LP Models with PolyhedralFunctions
 =======================================
 
-We could build a vector of :code:`JuMP.Model` with a vector of :code:`PolyhedralFunction` to perform simulation. For this, use the function::
+We can build a vector of :code:`JuMP.Model` with a vector of :code:`PolyhedralFunction` to perform simulation. For this, use the function::
 
     problems = StochDynamicProgramming.hotstart_SDDP(model, param, V)
 
 
 SDDP hotstart
 =============
 
-If cuts are already available, we could hotstart SDDP while overloading the function :code:`solve_SDDP`::
+If cuts are already available, we can hotstart SDDP while overloading the function :code:`solve_SDDP`::
 
     V, pbs = solve_SDDP(model, params, 0, V)