Csdp, a C Library for Semideenite Programming

A number of codes for semide nite programming SDP are already available in cluding Why introduce yet another code for SDP CSDP is written in C for e ciency and portability The code is designed to make use of highly optimized linear algebra routines from the LINPACK or LAPACK libraries CSDP is distributed with version of the necessary LINPACK routines that have been translated into C The package also includes an optimized version of the BLAS routine DGEMM CSDP is designed to handle constraint matrices with general sparse structure CSDP can accommodate linear inequality constraints as well as linear equality constraints In addition to its SDP solver the CSDP library contains routines for reading and writing SDP problems and solutions The code has been designed for use both as a stand alone solver and as a callable subroutine for use within larger programs that require the solution of SDP subproblems We present results from the solution of the SDPLIB test problems CSDP has also been used in a code for the solution of MAX SAT problems The remainder of this paper is organized as follows First we discuss the formula tion of the semide nite programming problem used by CSDP We then describe the predictor corrector algorithm used by CSDP to solve the SDP We discuss the stor age requirements of the algorithm as well as its computational complexity Finally we present results from the solution of a number of test problems