Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Computational Optimization and Applications
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Interior Methods for Nonlinear Optimization
SIAM Review
Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Primal-Dual Interior Methods for Nonconvex Nonlinear Programming
SIAM Journal on Optimization
Parallel Computing - Parallel matrix algorithms and applications
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
A globally convergent primal-dual interior-point filter method for nonlinear programming
Mathematical Programming: Series A and B
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence
SIAM Journal on Optimization
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM Journal on Matrix Analysis and Applications
Mathematical Programming: Series A and B
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
SIAM Journal on Scientific Computing
Face image relighting using locally constrained global optimization
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Direct sparse factorization of blocked saddle point matrices
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
A blendshape model that incorporates physical interaction
Computer Animation and Virtual Worlds
Approximate weighted matching on emerging manycore and multithreaded architectures
International Journal of High Performance Computing Applications
Efficient Numerical Methods for Strongly Anisotropic Elliptic Equations
Journal of Scientific Computing
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
Hi-index | 0.00 |
Interior-point methods are among the most efficient approaches for solving large-scale nonlinear programming problems. At the core of these methods, highly ill-conditioned symmetric saddle-point problems have to be solved. We present combinatorial methods to preprocess these matrices in order to establish more favorable numerical properties for the subsequent factorization. Our approach is based on symmetric weighted matchings and is used in a sparse direct LDL T factorization method where the pivoting is restricted to static supernode data structures. In addition, we will dynamically expand the supernode data structure in cases where additional fill-in helps to select better numerical pivot elements. This technique can be seen as an alternative to the more traditional threshold pivoting techniques. We demonstrate the competitiveness of this approach within an interior-point method on a large set of test problems from the CUTE and COPS sets, as well as large optimal control problems based on partial differential equations. The largest nonlinear optimization problem solved has more than 12 million variables and 6 million constraints.