Discussion on the convergence of Rosen's gradient projection method (Q578858)

Since \textit{J. B. Rosen}'s gradient projection method was published [J. Soc. Industr. Appl. Math. 8, 181-217 (1960; Zbl 0099.364)], a rigorous convergence proof of the method has remained to be an open question. A convergence proof for the three dimensional case is given in this paper. The whole proof, except one lemma which we failed to prove for the general case, is applicable to the general case. For the general case a convergence condition is given in the main theorem.