Practical Anti-cycling Procedure for Linear and Nonlinear Programming

A new method is given for preventing the simplex method from cycling. Key features are that a positive step is taken at every iteration, and nonbasic variables are allowed to be slightly infeasible. There is no additional work per iteration. Computational results are given for the first 53 test problems in netlib, indicating reliable performance in all cases. The method may be applied to active-set methods for solving nonlinear programs with linear constraints. Keywords: EXPAND procedure, EXPAND(Expanding Tolerance Anti-Degeneracy), Optimization. (kr).