TY - JOUR

T1 - How to generate weakly infeasible semidefinite programs via Lasserre's relaxations for polynomial optimization

AU - Waki, Hayato

N1 - Funding Information:
Acknowledgments We would like to thank Prof. Masakazu Muramatsu and an anonymous reviewer for very helpful comments. The author was supported by Grant-in-Aid for Young Scientists (B) 22740056.
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012/11

Y1 - 2012/11

N2 - Examples of weakly infeasible semidefinite programs (SDP) are useful to test whether SDP solvers can detect infeasibility. However, finding non trivial such examples is notoriously difficult. This note shows how to use Lasserre's semidefinite programming relaxations for polynomial optimization in order to generate examples of weakly infeasible SDP. Such examples could be used to test whether a SDP solver can detect weak infeasibility. In addition, in this note, we generate weakly infeasible SDP from an instance of polynomial optimization with nonempty feasible region and solve them by SDP solvers. Although all semidefinite programming relaxation problems are infeasible, we observe that SDP solvers do not detect the infeasibility and that values returned by SDP solvers are equal to the optimal value of the instance due to numerical round-off errors.

AB - Examples of weakly infeasible semidefinite programs (SDP) are useful to test whether SDP solvers can detect infeasibility. However, finding non trivial such examples is notoriously difficult. This note shows how to use Lasserre's semidefinite programming relaxations for polynomial optimization in order to generate examples of weakly infeasible SDP. Such examples could be used to test whether a SDP solver can detect weak infeasibility. In addition, in this note, we generate weakly infeasible SDP from an instance of polynomial optimization with nonempty feasible region and solve them by SDP solvers. Although all semidefinite programming relaxation problems are infeasible, we observe that SDP solvers do not detect the infeasibility and that values returned by SDP solvers are equal to the optimal value of the instance due to numerical round-off errors.

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U2 - 10.1007/s11590-011-0384-1

DO - 10.1007/s11590-011-0384-1

M3 - Article

AN - SCOPUS:84869493785

VL - 6

SP - 1883

EP - 1896

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 8

ER -