Plans for Maximacomponents regarding linear autarkies.
More...
Go to the source code of this file.
Detailed Description
Plans for Maximacomponents regarding linear autarkies.
 Todo:
 Finding linear autarkies

DONE (predicate laut_paocs_p) Given the clausevariable matrix M, nontrival linear autarkies are given as nontrivial solutions of M x >= 0.

DONE (helper functions are provided by us) From what Maxima provides, apparently only maximize_lp (in package "simplex") is of use.

DONE (find_linearautarky_ocs) One possibility to achieve complete search for linear autarkies is to consider one after another the additional constraints x_i >= 1 and x_i <= 1.

An alternative is to first consider balanced linear autarkies (by linear equations, i.e., M x = 0), and then solving all M x = e_i for the possible e_i.

In both cases the objective function would be constant zero.

The above methods just search for feasible solutions. How can we use the optimisation facilities? Apparently only heuristical usage is possible?

For example maximising the sum of all x_i.

If this only yields 0, then one can attempt minimising the sum of the x_i.

What can be said in the remaining case? All solutions fulfill sum x_i = 0; is this possible if we also know that no balanced autarkies (nontrivial solutions of M x = 0) exist?

Finally we need a dedicated approach.

M has a nontrival linear autarky iff the polyhedron M x >= 0 is unbounded, and a nontrivial linear autarky corresponds to an infinite ray contained in the polyhedron. Can this be better exploited?
Definition in file LinearAutarkies.hpp.