The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation

Let A be a real symmetric positive definite n × n matrix and b a real column n-vector. We consider the following problem: Find real column n-vectors x and y such that \[{ A}{ x} = { b} + { y},\]\[{ x}^T { y} = 0, { x} 0, { y} 0.\] Problems of this type occur when the method of Christopherson is used to solve free boundary problems for journal bearings. In such cases, A is a “finite difference" matrix. We present a method for solving the above problem which is a modification of systematic over-relaxation. This method is particularly suitable when A is a finite difference matrix.