An alternating projections method for certain linear problems in a Hilbert space

Recent extensions of von Neumann's alternating projection methodpermit the computation of proximity projections onto certainconvex sets. This paper exploits this fact in constructing aglobally convergent method for minimizing linear functions overa convex set in a Hilbert space. In particular, we solve theeducational testing problem and an inverse eigenvalue problem,two difficult problems involving positive semidefiniteness constraints.