GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Preconditioners for indefinite systems arising in optimization
SIAM Journal on Matrix Analysis and Applications
Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem
SIAM Journal on Numerical Analysis
Software for simplified Lanczos and QMR algorithms
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
Primal-dual interior-point methods
Primal-dual interior-point methods
Matrix-Dependent Multigrid Homogenization for Diffusion Problems
SIAM Journal on Scientific Computing
Multigrid
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Convex Optimization
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
SIAM Journal on Scientific Computing
Steering exact penalty methods for nonlinear programming
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Adaptive Barrier Update Strategies for Nonlinear Interior Methods
SIAM Journal on Optimization
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We develop and compare multilevel algorithms for solving constrained nonlinear variational problems via interior point methods. Several equivalent formulations of the linear systems arising at each iteration of the interior point method are compared from the point of view of conditioning and iterative solution. Furthermore, we show how a multilevel continuation strategy can be used to obtain good initial guesses (“hot starts”) for each nonlinear iteration. Some minimal surface and volume-constrained image registration problems are used to illustrate the various approaches.