EXPOSING CONSTRAINTS

The development of algorithms and software for the solution of large-s cale optimization problems has been the main motivation behind the res earch on the identification properties of optimization algorithms. The aim of an identification result for a linearly constrained problem is to show that if the sequence generated by an optimization algorithm c onverges to a stationary point, then there is a nontrivial face F of t he feasible set such that after a finite number of iterations, the ite rates enter and remain in the face F. This paper develops the identifi cation properties of linearly constrained optimization algorithms with out any nondegeneracy or linear independence assumptions. The main res ult shows that the projected gradient converges to zero if and only if the iterates enter and remain in the face exposed by the negative gra dient. This result generalizes results of Burke and More obtained for nondegenerate cases.