Dual method for linear programs

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

This is a basic functionality of Linear Program which has to be implemented in Sage. This function could use the functions defined in libraries such as GLPK or CBC.

http://en.wikipedia.org/wiki/Linear_programming

Update:

This old ticket is somewhat vague. Some clarification.

• For simplex-based solvers, there should be facilities for extracting dual information from the optimal dictionary. Some backends already provide functions like get_row_dual (GLPK); #18804 provides a way to expose this information in a more high-level way.
• For simplex-based solvers, there should be a way to explicitly request using the primal or the dual simplex method. For GLPK, this is possible using solver parameter "primal_v_dual". Other solvers support this too, but I don't think the Sage backends expose it. Ideally, there should be a backend-independent way to request a particular method.

CC: @sagetrac-r-gaia-cs

Component: linear programming

Issue created by migration from https://trac.sagemath.org/ticket/7290

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,10 @@
 This is a basic functionality of Linear Program which has to be implemented in Sage. This function could use the functions defined in libraries such as GLPK or CBC.

 http://en.wikipedia.org/wiki/Linear_programming
+
+Update:
+
+This old ticket is somewhat vague. Some clarification.
+- For simplex-based solvers, there should be facilities for extracting dual information from the optimal dictionary. Some backends already provide functions like `get_row_dual` (GLPK); #18804 provides a way to expose this information in a more high-level way.
+- For simplex-based solvers, there should be a way to explicitly request using the primal or the dual simplex method. For GLPK, this is possible using solver parameter "primal_v_dual". Other solvers support this too, but I don't think the Sage backends expose it. Ideally, there should be a backend-independent way to request a particular method.
+