D-optimal matrices via quadratic integer optimization
- 181 Downloads
We show how to express the problem of searching for D-optimal matrices as a Linear and Quadratic Integer Optimization problem. We also focus our attention in the case where the size of the circulant submatrices that are used to construct a D-optimal matrix is a multiple of 3. In this particular case, we describe some additional combinatorial and number-theoretic characteristics that a solution of the D-optimal matrix problem must possess. We give some solutions for some quite challenging D-optimal matrix problems that can be used as benchmarks to test the efficiency of Linear and Quadratic Integer Optimization algorithms.
KeywordsPeriodic autocorrelation function Linear and quadratic integer optimization Algorithms
Unable to display preview. Download preview PDF.
- Floudas, C.A., Pardalos, P.M. (eds.): Encyclopedia of Optimization, vols. I–VI. Kluwer Academic, Dordrecht (2001) Google Scholar
- Kharaghani, H., Orrick, W.: D-optimal matrices. In: Colbourn, C.J., Dinitz, J.H. (eds.) Handbook of Combinatorial Designs, 2nd edn. Discrete Mathematics and Its Applications. Chapman & Hall/CRC, Boca Raton (2007) Google Scholar
- Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.): Handbook of Semidefinite Programming. Theory, Algorithms, and Applications. International Series in Operations Research & Management Science, vol. 27. Kluwer Academic, Boston (2000) Google Scholar