The Definition and Generation of Geometrically Random Linear Constraint Sets

The conventional procedure for generating random linear constraint sets independently and uniformly selects the constraint coefficients. Structure is usually imposed through some kind of rejection technique. Recent work of Van Dam and Telgen indicates that this type of generator tends to produce geometrically atypical polvtopes. We define and construct a generator that produces geometrically random constraint sets; that is, their probability measure is invariant to the choice of coordinate system used. Moreover, an extremely efficient technique is presented for making an unbiased selection of a feasible polytope. Conventional approaches often guarantee feasibility by implicitly selecting that randomly generated polytope covering the origin. Such a procedure hisses the selection in favor of large polytopes.