[docs] basic math almost completed. Added figures, and rspapproaches.

convexengineering · Jun 26, 2019 · fc0ad2f · fc0ad2f
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diff --git a/docs/source/index.rst b/docs/source/index.rst
@@ -29,6 +29,7 @@ Table of contents:
    whyro
    math
    methods
+   rspapproaches
    simulation
    goal
    references

diff --git a/docs/source/math.rst b/docs/source/math.rst
@@ -51,7 +51,7 @@ of posynomials.
 |picHsiung|
 
 .. |picHsiung| image:: picHsiung.png
-        :width: 70%
+        :width: 80%
 
 For derivation of robust GPs, the central finding is in Corollary 1 of the paper,
 which asserts that there is an analytical solution for the lowest-error
@@ -86,9 +86,32 @@ by adding auxiliary variables and using properties of inequalities.
 GPs have robust formulations.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+Since we can represent all posynomials as PWL functions, we can robustify
+GP inequalities. Note that equalities cannot be robustified like inequalities, since
+under perturbation they would be infeasible. As such, it is preferred that equalities
+are relaxed whenever possible in GP models that will be robustified.
+
+The final addition to this framework to enable robust GPs
+is to separate posynomials
+according to the dependence of monomial terms, as described in [Saab, 2018] and [Ozturk, 2019]. 
+We show an example of such a partition, borrowed from Ozturk et al.. 
+
+|partitioning|
+
+.. |partitioning| image:: partitioning.png
+        :width: 80%
 
 RSPs can be represented as sequential RGPs.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+Just as SPs are solved as a sequence of GPs, RSPs can be solved as a
+sequence of RGPs. We solve the nominal RSP, then use the solution
+as the initial guess for the RSP solution heuristic outlined below.
+
+|rspSolve|
+
+.. |rspSolve| image:: rspSolve.png
+        :width: 80%
 
-Work in progress...
+Within this framework, all GPs and SPs, given that they
+are feasible, have tractable robust counterparts.
diff --git a/docs/source/methods.rst b/docs/source/methods.rst
@@ -3,7 +3,8 @@ Robustification methods
 
 Within **robust**, there are 3 tractable approximate robust formulations for
 GPs and SPs. The methods are detailed at a high level below, in decreasing order of conservativeness.
-Please see [Saab, 2018] for further details.
+Please see [Saab, 2018] for further details. The following descriptions have been
+borrowed from [Ozturk, 2019].
 
 Simple Conservative Approximation
 ---------------------------------

diff --git a/docs/source/partitioning.PNG b/docs/source/partitioning.PNG
diff --git a/docs/source/picHsiung.PNG b/docs/source/picHsiung.PNG
diff --git a/docs/source/rspSolve.PNG b/docs/source/rspSolve.PNG
diff --git a/docs/source/rspapproaches.rst b/docs/source/rspapproaches.rst
@@ -0,0 +1,4 @@
+Approaches to solving robust SPs
+================================
+
+Work in progress...