Using approximate secant equations in limited memory methods for multilevel unconstrained optimization

作者：Gratton Serge; Malmedy Vincent; Toint Philippe L^*

来源：Computational Optimization and Applications, 2012, 51(3): 967-979.

DOI：10.1007/s10589-011-9393-3

• Nonlinear optimization
• Multilevel problems
• Quasi-Newton methods
• Nonlinear conjugate gradient methods
• Limited-memory algorithms

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.

• 出版日期2012-4