LogdetPPA version 0 -- a MATLAB software for log-determinant SDP based on a Newton-CG proximal point algorithm

Chengjing Wang, Defeng Sun, and Kim-Chuan Toh

The software is designed to solve standard primal and dual log-determinant SDPs of the form:
 (P)  min  (C1,X1) + ... + (CN,XN) - mu1*logdet(X1) - ... - muN*logdet(XN) 
      s.t. A1(X1) + ... + AN(XN) = b, 
           X1,...,XN positive definite

 (D)  max  (b,y) + mu1*logdet(Z1) + ... + muN*logdet(ZN) + constant 
      s.t. A1t(y) + Z1 = C1, ... ,ANt(y) + ZN = CN, 
           Z1,..,ZN positive definite

      where Xk, Zk are either symmetric positive definite matrices or positive vectors.  
      The parameters mu1,...,muN are given positive scalars. 
      The constant term in (D) depends on the dimension of X1,...,XN and mu1,...,muN. 
Important note: this is a research software. It is not intended nor designed to be a general purpose software at the moment.
This software package is designed for solving standard SDP problems with max{n1,...,nN} (nk=dimension of matrix variable Xk) up to 2000. The number of linear equality constraints (dimension of b) can be large, say, more than 100 thousands.
For more details, see:
  • Chengjing Wang, Defeng Sun, and Kim-Chuan Toh, Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm, SIAM J. Optimization, 20 (2010), pp. 2994--3013.