Representations of quasi-Newton matrices and their use in limited memory methods
Mathematical Programming: Series A and B
Computing modified Newton directions using a partial Cholesky factorization
SIAM Journal on Scientific Computing
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Multigrid
On the Behavior of the Gradient Norm in the Steepest Descent Method
Computational Optimization and Applications
Enriched Methods for Large-Scale Unconstrained Optimization
Computational Optimization and Applications
Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
Convex Optimization
Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
SIAM Journal on Scientific Computing
A Multigrid Scheme for Elliptic Constrained Optimal Control Problems
Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
SIAM Journal on Optimization
SIAM Journal on Numerical Analysis
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
Approximate invariant subspaces and quasi-newton optimization methods
Optimization Methods & Software
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We present a line search multigrid method for solving discretized versions of general unconstrained infinite-dimensional optimization problems. At each iteration on each level, the algorithm computes either a “direct search” direction on the current level or a “recursive search” direction from coarser level models. Introducing a new condition that must be satisfied by a backtracking line search procedure, the “recursive search” direction is guaranteed to be a descent direction. Global convergence is proved under fairly minimal requirements on the minimization method used at all grid levels. Using a limited memory BFGS quasi-Newton method to produce the “direct search” direction, preliminary numerical experiments show that our line search multigrid approach is promising.