Version: 1.0.6
Title: R Interface to DSDP Semidefinite Programming Library
Maintainer: Zhisu Zhu <zhuzhisu@alumni.stanford.edu>
Description: R interface to DSDP semidefinite programming library. The DSDP software is a free open source implementation of an interior-point method for semidefinite programming. It provides primal and dual solutions, exploits low-rank structure and sparsity in the data, and has relatively low memory requirements for an interior-point method.
Imports: utils, methods
LazyLoad: yes
License: GPL-3
URL: https://www.mcs.anl.gov/hs/software/DSDP
NeedsCompilation: yes
Packaged: 2025-06-08 15:41:18 UTC; root
Repository: CRAN
Date/Publication: 2025-06-08 16:20:02 UTC
Author: Zhisu Zhu [aut, cre], Yinyu Ye [aut] (DSDP by Steve Benson, Yinyu Ye and Xiong Zhang)

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

Solve semidefinite programm with DSDP

Description

Interface to DSDP semidefinite programming library.

Usage

dsdp(A,b,C,K,OPTIONS=NULL)

Arguments

A

An object of class "matrix" with m rows defining the block diagonal constraint matrices A_i. Each constraint matrix A_i is specified by a row of A as explained in the Details section.

b

A numeric vector of length m containg the right hand side of the constraints.

C

An object of class "matrix" with one row or a valid class from the class hierarchy in the "Matrix" package. It defines the objective coefficient matrix C with the same structure of A as explained above.

K

Describes the sizes of each block of the sdp problem. It is a list with the following elements:

"s":

A vector of integers listing the dimension of positive semidefinite cone blocks.

"l":

A scaler integer indicating the dimension of the linear nonnegative cone block.

OPTIONS

A list of OPTIONS parameters passed to dsdp. It may contain any of the following fields:

print:

= k to display output at each k iteration, else = 0 [default 10].

logsummary:

= 1 print timing information if set to 1.

save:

to set the filename to save solution file in SDPA format.

outputstats:

= 1 to output full information about the solution statistics in STATS.

gaptol:

tolerance for duality gap as a fraction of the value of the objective functions [default 1e-6].

maxit:

maximum number of iterations allowed [default 1000].

Please refer to DSDP User Guide for additional OPTIONS parameters available.

Details

All problem matrices are assumed to be of block diagonal structure, the input matrix A must be specified as follows:

  1. The coefficients for nonnegative cone block are put in the first K$l columns of A.

  2. The coefficients for positive semidefinite cone blocks are put after nonnegative cone block in the the same order as those in K$s. The ith positive semidefinite cone block takes (K$s)[i] times (K$s)[[i]] columns, with each row defining a symmetric matrix of size (K$s)[[i]].

This function does not check for symmetry in the problem data.

Value

Returns a list of three objects:

X

Optimal primal solution X. A vector containing blocks in the same structure as explained above.

y

Optimal dual solution y. A vector of the same length as argument b

STATS

A list with three to eight fields that describe the solution of the problem:

stype:

PDFeasible if the solutions to both (D) and (P) are feasible, Infeasible if (D) is infeasible, and Unbounded if (D) is unbounded.

dobj:

objective value of (D).

pobj:

objective value of (P).

r:

the multiple of the identity element added to C-\mathcal{A}^{*}y in the final solution to make S positive definite.

mu:

the final barrier parameter \nu.

pstep:

the final step length in (P)

dstep:

the final step length in (D)

pnorm:

the final value \| P(\nu)\|.

The last five fields are optional, and only available when OPTIONS$outputstats is set to 1.

References

Examples

	K=NULL
	K$s=c(2,3)
	K$l=2

	C=matrix(c(0,0,2,1,1,2,c(3,0,1,
                       0,2,0,
                       1,0,3)),1,15,byrow=TRUE)
	A=matrix(c(0,1,0,0,0,0,c(3,0,1,
                         0,4,0,
                         1,0,5),
          	1,0,3,1,1,3,rep(0,9)), 2,15,byrow=TRUE)
	b <- c(1,2)
	
    OPTIONS=NULL
    OPTIONS$gaptol=0.000001
    OPTIONS$logsummary=0
    OPTIONS$outputstats=1
	
    result = dsdp(A,b,C,K,OPTIONS)

Solving semidefinite programs reading from SDPA format files.

Description

Function to read the semidefinite program input data in SDPA format and solve it.

Usage

dsdp.readsdpa(sdpa_filename, options_filename="")

Arguments

sdpa_filename

The location of the SDPA input file.

options_filename

The location of the OPTIONS file [default ""].