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Verifying exactness of relaxations for robust semi-definite programs by solving polynomial systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dietz, Sjoerd G. Scherer, Carsten W. |
| Copyright Year | 2008 |
| Abstract | Abstract In this paper, robust semi-definite programs are considered with the goal of verifying whether a particular LMI relaxation is exact. A procedure is presented showing that verifying exactness amounts to solving a polynomial system. The main contribution of the paper is a new algorithm to compute all isolated solutions of a system of polynomials. Standard techniques in computational algebra, often referred to as Stetter’s method [H.J. Stetter, Numerical Polynomial Algebra, SIAM, 2004], involve the computation of a Grobner basis of the ideal generated by the polynomials and further require joint eigenvector computations in order to arrive at the zeros of the polynomial system. Our algorithm does neither require structural knowledge on the polynomial system, nor does it rely on the computation of joint eigenvectors. |
| Starting Page | 1758 |
| Ending Page | 1778 |
| Page Count | 21 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.laa.2008.05.009 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/82142828.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.laa.2008.05.009 |
| Volume Number | 429 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
