A convergence theorem of Rosen’s gradient projection method

Since Rosen’s gradient projection method was published in 1960, a rigorous convergence proof of his method has remained an open question. A convergence theorem is given in this paper. Part of this author’s work was done while he studied at the Department of Mathematics, University of California at Santa Barbara, and was supported by the National Science Foundation under Grant No. MCS83-14977. Part of this author’s work was done while he visited the Computer Science Department, University of Minnesota, Minneapolis, and was supported by the National Science Foundation under Grant No. MCS81-01214.