Degeneracy: Resolve or avoid?

Two projected gradient algorithms for linear programming are discussed. The first uses a conventional enough steepest edge approach, and implements a version of Wolfe’s method for resolving any problems of degeneracy. The second makes use of a steepest descent direction which is calculated by solving a linear least squares problem subject to bound constraints, and avoids problems of degeneracy altogether. They are compared using randomly generated problems which permit the specification of (known) degenerate minima. The results appear to favour the more conventional method as problem sizes get larger.