Interior-Point Gradient Methods with Diagonal-Scalings for Simple-Bound Constrained Optimization

In this paper, we study diagonally scaled gradient methods for simple-bound constrained optimization in a framework almost identical to that for unconstrained optimization, except that iterates are kept within the interior of the feasible region. We establish a satisfactory global convergence theory for such interior-point gradient methods applied to Lipschitz continuously differentiable functions without any further assumption. Moreover, a strong convergence result is obtained for a class of so-called L-nonlinear functions introduced in this paper which includes virtually all nonlinear functions that do not contain linear pieces.