Codes under the Matrix Optimization Project

QSDPNAL (version 1.0): a MATLAB software for solving convex quadratic semidefinite programming (QSDP) (click here for an introduction on how to use the package) [CAUTION: this software is for research purpose. It is neither intended nor designed to be a general purpose software at the moment.] For the details of the software, please check the following papers:

[Xudong Li, Defeng Sun, and Kim Chuan Toh, “QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming”, Mathematical Programming Computation, 10 (2018) 703–743.]

[Xudong Li, Defeng Sun, and Kim Chuan Toh, “A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications”, Mathematical Programming 175 (2019) 395–418. arXiv:1703.06629]

SDPNAL+: a MATLAB software for solving large scale semidefinite programming with bound constraints (click here for an introduction on how to use the package) [awarded the triennial Beale–Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society at Bordeaux, France, July 2-6, 2018. See Picture 1, Picture 2, and Picture 3.] [CAUTION: this software is NOT designed for solving small to medium sized SDP problems, for which interior point methods based software such as SDPT3 is a better option.] For the details of the software, please check the following papers:

[Defeng Sun, Kim Chuan Toh, Y.C. Yuan, Xinyuan Zhao, SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0), to appear in Optimization Methods and Software (2019).]

[Liuqin Yang, Defeng Sun, and Kim Chuan Toh, SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints, Mathematical Programming Computation, 7 (2015), pp. 331-366.]

[Defeng Sun, Kim Chuan Toh, and Liuqin Yang, “A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type constraints”, SIAM Journal on Optimization Vol. 25, No. 2 (2015) 882–915. Detailed computational results for over 400 problems tested in the paper. You may also find a supplementary note here on more detailed comparisons between the performance of our proposed algorithm and various variants of ADMMs.]

[Xinyuan Zhao, D.F. Sun, and Kim Chuan Toh, A Newton-CG augmented Lagrangian method for semidefinite programming, SIAM Journal on Optimization, 20 (2010), pp. 1737–1765.]

“Solving log-determinant optimization problems by a Newton-CG proximal point algorithm”. See the brief user’s guide logdet-0-guide.pdf.

CorMatHdm_general.m Computing the H-weighted Nearest Correlation Matrix with fixed elements and lower and upper bounds [H should not have too many zero elements for better numerical performance; otherwise, see CaliMatHdm] Testing example: testCorMatHdm_general.m (uploaded on September 14, 2009).

CaliMatHdm.zip Calibrating the H-weighted Nearest Covariance Matrix [H is allowed to have a large number of zero elements] (uploaded in April 2010).