R: R interface to DSDP semidefinite programming library

Rdsdp {Rdsdp} | R Documentation

## 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

inf tr(CX)

subject to AX = b

X >= 0

with (AX)_i = tr(A_iX) where X >= 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

sup b'y

subject to A'y + S = C

S >= 0

where A'y = ∑_{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

[Package Rdsdp version 1.0.5.2 Index]