Paper Info
Title
Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization
Abstract
We observe that in a simple one-dimensional polynomial optimization problem (POP), the `optimal' values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial evidences for the strange behaviors of the SDP solvers are given. This result gives a warning to users of the SDP relaxation method for POPs to be careful in believing the results of the SDP solvers. We also demonstrate how SDPA-GMP, a multiple precision SDP solver developed by one of the authors, can deal with this situation correctly.
Year
DOI
Venue
2012
10.1007/s10589-011-9437-8
Comp. Opt. and Appl.
Keywords
Field
DocType
Polynomial optimization,Semidefinite programming,Numerical stability
Polynomial optimization,Mathematical optimization,Relaxation (iterative method),Solver,Interior point method,Mathematics,Semidefinite programming,Numerical stability
Journal
Volume
Issue
ISSN
53
3
0926-6003
Citations 
PageRank 
References 
10
0.75
12
Authors
3
Name
Order
Citations
PageRank
Hayato Waki137628.82
Maho Nakata2253.85
Masakazu Muramatsu333628.68