Computational Optimization and Applications
A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming
Computational Optimization and Applications
Primal-dual Newton-type interior-point method for topology optimization
Journal of Optimization Theory and Applications
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Computational Experience with Ill-Posed Problems in Semidefinite Programming
Computational Optimization and Applications
Best ellipsoidal relaxation to solve a nonconvex problem
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming
Computational Optimization and Applications
Solving semidefinite programming problems via alternating direction methods
Journal of Computational and Applied Mathematics
The Q method for second order cone programming
Computers and Operations Research
A refined theorem concerning the conditioning of semidefinite programs
Journal of Applied Mathematics and Computing
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
Optimization Methods & Software
Journal of Computational Physics
Matrix-lifting semi-definite programming for detection in multiple antenna systems
IEEE Transactions on Signal Processing
A continuous method for solving multiuser detection in CDMA
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
ACM Transactions on Mathematical Software (TOMS)
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
High-performance general solver for extremely large-scale semidefinite programming problems
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Strong duality and minimal representations for cone optimization
Computational Optimization and Applications
Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming
Numerical Algorithms
A homotopy method for nonlinear semidefinite programming
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Hi-index | 0.01 |
Primal-dual interior-point path-following methods for semidefinite programming are considered. Several variants are discussed, based on Newton's method applied to three equations: primal feasibility, dual feasibility, and some form of centering condition. The focus is on three such algorithms, called the XZ, XZ+ZX, and Q methods. For the XZ+ZX and Q algorithms, the Newton system is well defined and its Jacobian is nonsingular at the solution, under nondegeneracy assumptions. The associated Schur complement matrix has an unbounded condition number on the central path under the nondegeneracy assumptions and an additional rank assumption. Practical aspects are discussed, including Mehrotra predictor-corrector variants and issues of numerical stability. Compared to the other methods considered, the XZ+ZX method is more robust with respect to its ability to step close to the boundary, converges more rapidly, and achieves higher accuracy.