Adjoint-based optimization of PDE systems with alternative gradients
Journal of Computational Physics
Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines
Computers and Operations Research
A multilevel algorithm for solving the trust-region subproblem
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
A Line Search Multigrid Method for Large-Scale Nonlinear Optimization
SIAM Journal on Optimization
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
SIAM Journal on Optimization
Line Search Multilevel Optimization as Computational Methods for Dense Optical Flow
SIAM Journal on Imaging Sciences
Scalable vectorless power grid current integrity verification
Proceedings of the 50th Annual Design Automation Conference
Using inexact gradients in a multilevel optimization algorithm
Computational Optimization and Applications
| Hi-index | 0.01 |
We discuss a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems appear in many applications and are of a different nature than systems of equations. Our approach uses an optimization-based multigrid algorithm in which the multigrid algorithm relies explicitly on nonlinear optimization models as subproblems on coarser grids. Our goal is not to argue for a particular optimization-based multigrid algorithm, but instead to demonstrate how multigrid can be used to accelerate nonlinear programming algorithms. Furthermore, using several model problems we give evidence (both theoretical and numerical) that the optimization setting is well suited to multigrid algorithms. Some of the model problems show that the optimization problem may be more amenable to multigrid than the governing differential equation. In addition, we relate the multigrid approach to more traditional optimization methods as further justification for the use of an optimization-based multigrid algorithm.