Robbie, On the wikibook page http://en.wikibooks.org/wiki/GLPK/Solution_information I noticed some incorrectness in the topic "KKT report". The correct explanation is the following:
KKT.PE shows an absolute and relative error in solution of the primal system of equality constraints xR - A xS = 0, where xR is the vector of auxiliary variables, xS is the vector of structural variables, A is the original constraint matrix. KKT.PB shows errors in primal feasibility, that is, bound violation for primal variables l <= x <= u, where x is the vector of all variables, l are lower bounds, u are upper bounds. KKT.DE shows errors in solution of the dual system of equality constraints A'lambdaR + lambdaS = c, where lambdaR is the vector of reduced costs of auxiliary variables, lambdaS is the vector of reduced costs of structural variables, A' is a matrix transposed to the original constraint matrix, and c is the original vector of constraint coefficients. KKT.DB shows errors in dual feasibility (non-optimality), that is, bound violation for dual variables lambda >= 0, <= 0, or = 0 (depending on the type of bounds of corresponding auxiliary and structural variables), where lambda is the vector of Lagrangian multipliers (reduced costs). Please see formulae (3.14)-(3.19) in Section 4.1 of the glpk reference manual. Best regards, Andrew Makhorin _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk
