update doc for slack models.

syarra · dpo · commit 316a8ac0af4c · 2016-10-15T13:54:06.000-04:00
diff --git a/doc/source/modeling.rst b/doc/source/modeling.rst
@@ -127,67 +127,6 @@ The :mod:`snlp` Module
 
 .. automodule:: snlp
 
-
-`SlackFramework` is a general framework for converting the :ref:`general
-nonlinear optimization problem <nlp>` to a form using slack variables.
-
-The transformed problem is in the variables `x`, `s` and `t` and its
-constraints have the form
-
-.. math::
-
-    c_i(x) - a_i = 0, & \qquad i = 1, \ldots, m, \\
-    g_j(x) - g_j^L - s_j^L = 0, & \qquad j = 1, \ldots, p,
-    \qquad \text{for which} \quad  g_j^L > -\infty, \\
-    s_j^L \geq 0, & \qquad j = 1, \ldots, p,
-    \qquad \text{for which} \quad g_j^L > -\infty, \\
-    g_j^U - g_j(x) - s_j^U = 0, & \qquad j = 1, \ldots, p,
-    \qquad \text{for which} \quad g_j^U < +\infty, \\
-    s_j^U \geq 0, & \qquad j = 1, \ldots, p,
-    \qquad \text{for which} \quad g_j^U < +\infty, \\
-    x_k - x_k^L - t_k^L = 0, & \qquad k = 1, \ldots, n,
-    \qquad \text{for which} \quad x_k^L > -\infty, \\
-    t_k^L \geq 0, & \qquad k = 1, \ldots, n,
-    \qquad \text{for which} \quad x_k^L > -\infty, \\
-    x_k^U - x_k - t_k^U = 0, & \qquad k = 1, \ldots, n,
-    \qquad \text{for which} \quad x_k^U < +\infty, \\
-    t_k^U \geq 0, & \qquad k = 1, \ldots, n,
-    \qquad \text{for which} \quad x_k^U < +\infty.
-
-In the latter problem, the only inequality constraints are bounds on
-the slack variables. The other constraints are (typically) nonlinear
-equalities.
-
-The order of variables in the transformed problem is as follows:
-
-[  x  |  sL  |  sU  |  tL  |  tU  ]
-
-where:
-
-- sL = [ sLL | sLR ], sLL being the slack variables corresponding to
-  general constraints with a lower bound only, and sLR being the slack
-  variables corresponding to the 'lower' side of range constraints.
-
-- sU = [ sUU | sUR ], sUU being the slack variables corresponding to
-  general constraints with an upper bound only, and sUR being the slack
-  variables corresponding to the 'upper' side of range constraints.
-
-- tL = [ tLL | tLR ], tLL being the slack variables corresponding to
-  variables with a lower bound only, and tLR being the slack variables
-  corresponding to the 'lower' side of two-sided bounds.
-
-- tU = [ tUU | tUR ], tUU being the slack variables corresponding to
-  variables with an upper bound only, and tLR being the slack variables
-  corresponding to the 'upper' side of two-sided bounds.
-
-This framework initializes the slack variables sL, sU, tL, and tU to
-zero by default.
-
-Note that the slack framework does not update all members of AmplModel,
-such as the index set of constraints with an upper bound, etc., but
-rather performs the evaluations of the constraints for the updated
-model implicitly.
-
 .. autoclass:: SlackModel
    :show-inheritance:
    :members:
diff --git a/nlp/model/snlp.py b/nlp/model/snlp.py
@@ -1,35 +1,36 @@
+# -*- coding: utf-8 -*-
 """A slack framework for NLP.py."""
 
 
 import numpy as np
 from nlp.model.nlpmodel import NLPModel
-from pysparse.sparse.pysparseMatrix import PysparseMatrix as sp
 
 __docformat__ = 'restructuredtext'
 
 
 class SlackModel(NLPModel):
-    """
-    General framework for converting a nonlinear optimization problem to a
+    u"""General framework for converting a nonlinear optimization problem to a
     form using slack variables.
 
-    Original problem:
-         cL <= c(x)
-               c(x) <= cU
-        cRL <= c(x) <= cRU
-        c(x) = cE
-        l <= x <= u
+    Original problem::
+
+         cᴸ ≤ c(x)
+              c(x) ≤ cᵁ
+        cᴿᴸ ≤ c(x) ≤ cᴿᵁ
+              c(x) = cᴱ
+          l ≤   x  ≤ u
+
+    is transformed to::
 
-    is transformed to:
+        c(x) - sᴸ = 0
+        c(x) - sᵁ = 0
+        c(x) - sᴿ = 0
+        c(x) - cᴱ = 0
 
-        c(x) - sL = 0
-        c(x) - sU = 0
-        c(x) - sR = 0
-        c(x) - cE = 0
-        cL  <= sL
-               sU <= cU
-        cRL <= sR <= cRU
-        l <= x <= u
+         cᴸ ≤ sᴸ
+              sᵁ ≤ cᵁ
+        cᴿᴸ ≤ sᴿ ≤ cᴿᵁ
+          l ≤ x  ≤ u
 
     In the latter problem, the only inequality constraints are bounds on the
     slack and original variables. The other constraints are (typically)
@@ -39,13 +40,13 @@ class SlackModel(NLPModel):
 
     1. x, the original problem variables.
 
-    2. sL, the slack variables corresponding to general constraints with
+    2. sᴸ, the slack variables corresponding to general constraints with
        a lower bound only.
 
-    3. sU, the slack variables corresponding to general constraints with
+    3. sᵁ, the slack variables corresponding to general constraints with
        an upper bound only.
 
-    4. sR, the slack variables corresponding to general constraints with
+    4. sᴿ, the slack variables corresponding to general constraints with
        a lower bound and an upper bound.
 
     This framework initializes the slack variables sL and sU to
@@ -55,13 +56,16 @@ class SlackModel(NLPModel):
     such as the index set of constraints with an upper bound, etc., but
     rather performs the evaluations of the constraints for the updated
     model implicitly.
-
-    :parameters:
-        :model:  Original model to be transformed into a slack form.
-
     """
 
     def __init__(self, model, **kwargs):
+        """Initialize a slack form of an :class:`NLPModel`.
+
+        :parameters:
+
+            :model:  Original model to be transformed into a slack form.
+
+        """
         self.model = model
 
         # Save number of variables and constraints prior to transformation
