Given a set ¦[ of Rn and a function f from ¦[ into Rn the authors consider a problem of finding a point x* in ¦[ such that (x-x*)tf(x*)≥0 holds for every point x in ¦[. This problem is called the stationary point problem and the point x* is called a stationary point. They present a variable dimension algorithm for solving the stationary point problem with an affine function f on a polytope ¦[ defined by constraints of linear equations and inequalities. The authors propose a system of equations whose solution set contains a piecewise linear path connecting a trivial starting point in ¦[ with a stationary point. The path can be followed by solving a series of linear programs which inherit the structure of constraints of ¦[. The linear programs are solved efficiently with the Dantzig-Wolfe decomposition method by exploiting fully the structure.
