The properties of multilevel optimization problems defined on a hierarchy of discretization grids can be used to define approximate secant equations, which describe the second-order behavior of the objective function. Following earlier work by Gratton and Toint (2009) we introduce a quasi-Newton method (with a linesearch) and a nonlinear conjugate gradient method that both take advantage of this new second-order information. We then present numerical experiments with these methods and formulate recommendations for their practical use. © Springer Science+Business Media, LLC 2011.
- nonlinear conjugate gradient methods
- nonlinear optimization
- quasi-Newton methods
- multilevel problems
- limited-memory algorithms
Gratton, S., Malmedy, V., & Toint, P. (2012). Using approximate secant equations in limited memory methods for multilevel unconstrained optimization. Computational Optimization and Applications, 51(3), 967-979. https://doi.org/10.1007/s10589-011-9393-3