We present some industrial problems arising from the optimal design of ophtalmic lenses, called Progressive Addition Lenses (PAL). These lenses are designed for correcting presbyopia, which is an eye condition that occurs after the middle-age. Presbyopia is caused by lack of accommodation of the eye. As the eye lens becomes older, it loses some elasticity and ability to change curvature to focus on near objects. We define the lens design problem as a constrained nonlinear least squares problem. We develop nonlinear algorithms following an interior points approach using Sequential Quadratic Programming and the trust region technique. Some comparisons are made between SQP algorithms based on active set strategies and a primal-dual line search algorithm. We present and analyse a quasi-newtonian preconditioning technique for a truncated Newton algorithm using the trust region technique.

Keywords:
Non linear optimization, interior points, trust region, truncated Newton methods, quasi-newtonian preconditionning, progressive addition lens design.