Affine scaling Interior Point methods for linear and nonlinear bound-constrained least-squares problems

Many applications, e.g. nonnegative image restoration, contact problems for mechanical systems, control problems, optimization of energy systems, plasma physics, chemical engineering, involve the numerical solution of bound-constrained least-squares problems. In this talk we will describe second order methods for this class of problems, focusing on Affine Scaling Interior Point approaches. These methods are globally convergent and can be applied both to linear and nonlinear problems. They provide fast local convergence also to degenerate points. We will focus on the linear algebra phase discussing how in case of large scale problems the linear systems can be efficiently handled by iterative linear solvers. Numerical results will be shown along with available software based on these approaches.