Rdsdp {Rdsdp}

R interface to DSDP semidefinite programming library

Description

Rdsdp is the R package providing a R interface to DSDP semidefinite programming library. The DSDP package implements a dual-scaling algorithm to find solutions (X, y) to linear and semidefinite optimization problems of the form

\mbox{(P)} \ \inf\, \mbox{tr}(CX)

\mbox{subject to}\; \mathcal{A}X = b

X \succeq 0

with (\mathcal{A}X)_i = \mbox{tr}(A_iX) where X \succeq 0 means X is positive semidefinite, C and all A_i are symmetric matrices of the same size and b is a vector of length m.

The dual of the problem is

\mbox{(D)} \ \sup\, b^{T}y

\mbox{subject to}\; \mathcal{A}^{*}y + S = C

S \succeq 0

where \mathcal{A}y = \sum_{i=1}^m y_i A_i.

Matrices C and A_i are assumed to be block diagonal structured, and must be specified that way (see Details).

References

• https://www.mcs.anl.gov/hs/software/DSDP/

• Steven J. Benson and Yinyu Ye:
  Algorithm 875: DSDP5 software for semidefinite programming ACM Transactions on Mathematical Software (TOMS) 34(3), 2008
  http://web.stanford.edu/~yyye/DSDP5-Paper.pdf

• Steven J. Benson and Yinyu Ye and Xiong Zhang:
  Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization SIAM Journal on Optimization 10(2):443-461, 2000
  http://web.stanford.edu/~yyye/yyye/largesdp.ps.gz