A superlinearly convergent method to linearly constrained optimization problems under degeneracy

Most papers concerning nonlinear programming problems with linear constraints assume linear independence of the gradients of the active constraints at any feasible point. In this paper we remove this assumption and give an algorithm and prove its convergency. Also, under appropriate assumptions on the objective function, including one which could be viewed as an extension of the strict complementary slackness condition at the optimal solution, we prove the rate of convergence of the algorithm to be superlinear.