Title :
A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP, -QD and -DD.
Author_Institution :
Adv. Center for Comput. & Commun., RIKEN, Saitama, Japan
Abstract :
Semidefinite programming (SDP) is an important branch of optimization and has wide range of applications: engineering, industry, chemistry, mathematics, etc. However, obtaining very accurate optimum for a semidefinite programming is difficult in general, especially for ill-posed ones. In this paper, we evaluated numerically highly accurate SDP solvers; SDPA-GMP, -QD and -DD, which employ multiple-precision arithmetic and mainly developed by our group. We applied to some problems from SDPLIB benchmark which contains some ill-posed problems as well. The SDPA-GMP, and -QD solved problems very accurately, whereas SDPA failed or obtained inaccurate optima. The SDPA-DD may be used for compensation for accuracy and speed. We also investigated the convergence behaviors which agreed well what theories indicated.
Keywords :
arithmetic; convergence of numerical methods; convex programming; SDPA-DD; SDPA-GMP; SDPA-QD; highly accurate multiple-precision arithmetic version; ill-posed problems; numerical evaluation; semidefinite programming; Accuracy; Convergence; Equations; IEEE standards; Libraries; Mathematical model; Programming;
Conference_Titel :
Computer-Aided Control System Design (CACSD), 2010 IEEE International Symposium on
Conference_Location :
Yokohama
Print_ISBN :
978-1-4244-5354-2
Electronic_ISBN :
978-1-4244-5355-9
DOI :
10.1109/CACSD.2010.5612693
