Computational Optimization and Applications
The minimum-rank gram matrix completion via modified fixed point continuation method
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Solving Log-Determinant Optimization Problems by a Newton-CG Primal Proximal Point Algorithm
SIAM Journal on Optimization
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
A projected semismooth Newton method for problems of calibrating least squares covariance matrix
Operations Research Letters
Leveraging Social Bookmarks from Partially Tagged Corpus for Improved Web Page Clustering
ACM Transactions on Intelligent Systems and Technology (TIST)
A Sequential Semismooth Newton Method for the Nearest Low-rank Correlation Matrix Problem
SIAM Journal on Optimization
ACM Transactions on Mathematical Software (TOMS)
Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming
Numerical Algorithms
Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
A trust region method for solving semidefinite programs
Computational Optimization and Applications
Computational Optimization and Applications
Lower bounds on the global minimum of a polynomial
Computational Optimization and Applications
Hi-index | 0.00 |
We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of the generalized Hessian of the objective function in these inner problems, a key property for ensuring the efficiency of using an inexact semismooth Newton-CG method to solve the inner problems, is equivalent to the constraint nondegeneracy of the corresponding dual problems. Numerical experiments on a variety of large-scale SDP problems with the matrix dimension $n$ up to $4,110$ and the number of equality constraints $m$ up to $2,156,544$ show that the proposed method is very efficient. We are also able to solve the SDP problem fap36 (with $n=4,110$ and $m=1,154,467$) in the Seventh DIMACS Implementation Challenge much more accurately than in previous attempts.