Computational Optimization and Applications
Updating the singular value decomposition
Journal of Computational and Applied Mathematics
Solving semidefinite programming problems via alternating direction methods
Journal of Computational and Applied Mathematics
Local Duality of Nonlinear Semidefinite Programming
Mathematics of Operations Research
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
A non-interior-point smoothing method for variational inequality problem
Journal of Computational and Applied Mathematics
Nonsingularity Conditions for the Fischer-Burmeister System of Nonlinear SDPs
SIAM Journal on Optimization
On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming
Journal of Global Optimization
Profile Arthur S. Bland: high performance at Oak Ridge laboratory
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
Matrix function: a "VIP" in linear algebra and its applications
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
A trust region method for solving semidefinite programs
Computational Optimization and Applications
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Motivated by some results for linear programs and complementarity problems, this paper gives some new characterizations of the central path conditions for semidefinite programs. Exploiting these characterizations, some smoothing-type methods for the solution of semidefinite programs are derived. The search directions generated by these methods are automatically symmetric, and the overall methods are shown to be globally and locally superlinearly convergent under suitable assumptions. Some numerical results are also included which indicate that the proposed methods are very promising and comparable to several interior-point methods. Moreover, the current method seems to be superior to the smoothing method recently proposed by Chen and Tseng [Non-interior continuation methods for solving semidefinite complementarity problems, {Technical report}, Department of Mathematics, University of Washington, Seattle, 1999].