Farid Alizadeh
RUTCOR, Rutgers University, New Brunswick, NJ.
E-mail: alizadeh@rutcor.rutgers.edu
Web: http://www.rutcor.edu/~alizadeh
Jean-Pierre
A. Haeberly
Department of Mathematics, Fordham University, Bronx, NY.
E-mail: haeberly@murray.fordham.edu
Madhu V. Nayakkankuppam
Courant Institute of Mathematical Sciences, New York University, NY.
E-mail: madhu@cs.nyu.edu
Web: http://www.cs.nyu.edu/phd_students/madhu
Michael L. Overton
Courant Institute of Mathematical Sciences, New York University, NY.
E-mail: overton@cs.nyu.edu
Web: http://www.cs.nyu.edu/faculty/overton
Stefan Schmieta
RUTCOR, Rutgers University, New Brunswick, NJ.
E-mail: schmieta@rutcor.rutgers.edu
Web: http://rutcor.rutgers.edu/~schmieta
This report describes SDPpack Version 0.9 Beta for Matlab 5.0.
This version extends the previous release for semidefinite programming (SDP)
to mixed semidefinite-quadratic-linear programs (SQLP),
i.e. linear optimization problems over a
product of semidefinite cones, quadratic cones and the nonnegative orthant.
Together, these cones make up all possible homogeneous self-dual cones
over the reals.
The main routine implements a primal-dual Mehrotra predictor-corrector
scheme based on the XZ+ZX search direction for SDP.
More specialized routines are also available, one to solve
SDP's with diagonal constraints only, and one to compute the Lovász
function of a graph, both using the XZ search direction.
Routines are also provided to determine whether an SQLP is primal or dual
degenerate at its solution and whether strict complementarity holds there.
Primal nondegeneracy is associated with dual uniqueness and dual
nondegeneracy with primal uniqueness, though these conditions are not
equivalent if strict complementarity fails to hold.
A routine is also provided to compute the condition number of an SQLP.
The Matlab code calls mex files for improved performance; binaries are
available for several platforms. Benchmarks show that the codes
provide highly accurate solutions to a wide variety of problems.
Copyright © 1997. All rights are reserved by the authors; restrictions in the copyright notice in each release also apply. SDPpack is software provided on an ``as is'' basis - no warranties, express or implied. In particular, the authors make no representation about the merchantability of this software or its fitness for any specific purpose. For research and noncommercial use: (i) this software is available free of charge, (ii) permission is granted to use, copy or distribute this software free of charge provided the copyright message in each release is preserved in each copy or distribution, (iii) permission is granted to modify this software provided every distribution or copy of the modified software contains a clear record of the modifications, and (iv) any publication resulting from research that made use of this software should cite this document.
This work was supported in part by the National Science Foundation.