SOLVING A CLASS OF LINEAR PROJECTION EQUATIONS

Many interesting and important constrained optimization problems in mathematical programming can be translated into an equivalent linear projection equation u = P(OMEGA)[u - (Mu + q)]. Here, P(OMEGA)(.) is the orthogonal projection on some convex set OMEGA (e.g. OMEGA = R+n) and M is a positive semidefinite matrix. This paper presents some new methods for solving a class of linear projection equations. The search directions of these methods are straighforward extensions of the directions in traditional methods for unconstrained optimization. Based on the idea of a projection and contraction method [7] we get a simple step length nile and are able to obtain global linear convergence.