Re: [Help-glpk] interpretation of 'glp_print_sol' and 'glp_print_ranges'

[Andrew Makhorin]

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