In most linear programming textbooks, the optimality conditions are refered to differently. They either use "weak duality" or "complementary slackness" when refering to the optimality conditions:
(1) weak duality is when there is a primal feasible solution, a dual feasible solution, and the primal objective value equals to the dual objective value (2) complementary slackness is where there is a primal feasible solution (x), a dual feasible solution (y), and whenever x_i is strictly between it's lower and upper bounds, the corresponding reduced cost as calculated with y is zero. Both these conditions are equivalent to the KKT, and in the linear programming case are fairly trivial to prove. But the textbooks don't usually call them KKT so I believe the wiki page entry should refer it as "Tests for Optimality" and then discuss the more precise calculations. I wish I had some time to write it up more... but I'm behind on doing some testing for Xypron and not sure when I'll get that finished. Maybe someone else can? -Marc -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Robbie Morrison Sent: Thursday, May 05, 2011 11:43 AM To: GLPK help Subject: [Help-glpk] GLPK wikibook : newish solution information page Hi all There is now a relatively new wikipage on solution information. I have a few small requests and hope people could oblige. Solution information http://en.wikibooks.org/wiki/GLPK/Solution_information - a general review please Karush-Kuhn-Tucker optimality conditions http://en.wikibooks.org/wiki/GLPK/Solution_information#Karush-Kuhn-Tucker_optimality_conditions - the "Requirement" table needs careful checking (noting that this is brief explanation!) Sensitivity analysis report http://en.wikibooks.org/wiki/GLPK/Solution_information#Sensitivity_analysis_report - the two "Rows" and "Columns" tables need careful checking - just a question (for my interest mostly): does this process involve re-solving the model using slightly different values? .. and if so, is it computationally expensive? Adaptive use http://en.wikibooks.org/wiki/GLPK/Solution_information#Adaptive_use - anyone care to contribute? Either make the changes directly, post back to this list, or email me off-line. TIA, Robbie --- Robbie Morrison PhD student -- policy-oriented energy system simulation Technical University of Berlin (TU-Berlin), Germany University email (redirected) : [email protected] Webmail (preferred) : [email protected] [from Webmail client] _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk This e-mail and any attachments may be confidential or legally privileged. If you received this message in error or are not the intended recipient, you should destroy the e-mail message and any attachments or copies, and you are prohibited from retaining, distributing, disclosing or using any information contained herein. Please inform us of the erroneous delivery by return e-mail. Thank you for your cooperation. _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk
