A conjugate gradient based affine scaling algorithm for bound constrained optimization

An affine scaling algorithm for bound constrained local optimization is proposed. Newton-Raphson is applied to the Coleman-Li first order optimality conditions, ultimately yielding a quadratic program with an ellipsoidal trust region. Instead of calculating the proposed step by solving this quadratic program exactly, the Steihaug-Toint conjugate gradients method is used to generate an approximate solution. It is shown the resulting method is almost immune to boundary proximity effects, and copes easily when the initial point is on the feasible region's boundary. Numerical results are generated for quadratics, quartics and a small number of standard test problems. These results show the method is effective.