Abstract
We apply the well-known MINLO outer-approximation algorithm (OA) to the maximum-entropy sampling problem (MESP), using the linx and NLP convex relaxations for MESP. We enhance our approach using disjunctive cuts.
M. Fampa was supported in part by CNPq grants 305444/2019-0 and 434683/2018-3. J. Lee was supported in part by AFOSR grant FA9550-19-1-0175 and ONR grant N00014-21-1-2135.
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References
Al-Thani, H., Lee, J.: MESgenCov (2020). github.com/hessakh/MESgenCov
Al-Thani, H., Lee, J.: An R package for generating covariance matrices for maximum-entropy sampling from precipitation chemistry data. SN Oper. Res. Forum 1, Article 17, 21 (2020)
Anstreicher, K.M.: Maximum-entropy sampling and the Boolean quadric polytope. J. Glob. Optim. 72, 603–618 (2018)
Anstreicher, K.M.: Efficient solution of maximum-entropy sampling problems. Oper. Res. 68, 1826–1835 (2020)
Anstreicher, K.M., Fampa, M., Lee, J., Williams, J.: Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems. Math. Program. Ser. A 85, 221–240 (1999)
Anstreicher, K.M., Lee, J.: A masked spectral bound for maximum-entropy sampling. In: Di Bucchianico, A., Läuter, H., Wynn, H.P. (eds.) mODa 7-Advances in Model-Oriented Design and Analysis. Contributions to Statistics, pp. 1–12. Physica, Heidelberg (2004). https://doi.org/10.1007/978-3-7908-2693-7_1
Balas, E.: Disjunctive programming. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-030-00148-3
Bonami, P., Linderoth, J., Lodi, A.: Disjunctive cuts for mixed integer nonlinear programming problems. In: Mahjoub, A. (ed.) Progress in Combinatorial Optimization, pp. 521–544. John Wiley & Sons Inc. (2011)
Burer, S., Lee, J.: Solving maximum-entropy sampling problems using factored masks. Math. Program. Ser. B 109, 263–281 (2007)
Chen, Z., Fampa, M., Lambert, A., Lee, J.: Mixing convex-optimization bounds for maximum-entropy sampling. Math. Prog. Ser. B 188, 539–568 (2021)
Chen, Z., Fampa, M., Lee, J.: On computing with some convex relaxations for the maximum-entropy sampling problem (2022). arxiv.org/abs/2112.14291
Choi, H.L., How, J., Barton, P.: An outer-approximation algorithm for generalized maximum entropy sampling. In: Proceedings of the ACC 2008, pp. 1818–1823. IEEE (2008)
Choi, H.L., How, J., Barton, P.: An outer-approximation approach for information-maximizing sensor selection. Optim. Lett. 7, 745–764 (2013)
Fedorov, V., Lee, J.: Design of experiments in statistics. In: Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.) Handbook of Semidefinite Programming. International Series in Operations Research & Management Science, vol. 27, pp. 511–532. Springer, Boston, MA (2000). https://doi.org/10.1007/978-1-4615-4381-7_17
Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327–349 (1994)
Guttorp, P., Le, N.D., Sampson, P.D., Zidek, J.V.: Using entropy in the redesign of an environmental monitoring network. In: Patil, G., Rao, C., Ross, N. (eds.) Multivariate Environmental Statistics, vol. 6, pp. 175–202. North-Holland (1993)
Hoffman, A., Lee, J., Williams, J. (2001). New upper bounds for maximum-entropy sampling. In: Atkinson, A.C., Hackl, P., Mäller, W.G. (eds.) mODa 6–Advances in Model-Oriented Design and Analysis. Contributions to Statistics, pp. 143–153. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57576-1_16
Ko, C.W., Lee, J., Queyranne, M.: An exact algorithm for maximum entropy sampling. Oper. Res. 43, 684–691 (1995)
Lee, J.: Constrained maximum-entropy sampling. Oper. Res. 46, 655–664 (1998)
Lee, J.: Maximum entropy sampling. In: El-Shaarawi, A., Piegorsch, W. (eds.) Encyclopedia of Environmetrics, 2nd ed., pp. 1570–1574. Wiley (2012)
Lee, J., Williams, J.: A linear integer programming bound for maximum-entropy sampling. Math. Program. Ser. B 94, 247–256 (2003)
Li, Y., Xie, W.: Best principal submatrix selection for the maximum entropy sampling problem: scalable algorithms and performance guarantees (2020). preprint at: https://arxiv.org/abs/2001.08537
Nikolov, A.: Randomized rounding for the largest simplex problem. In: Proceedings of STOC 2015, pp. 861–870. ACM, New York (2015)
Shewry, M.C., Wynn, H.P.: Maximum entropy sampling. J. Appl. Stat. 46, 165–170 (1987)
Toh, K.C., Todd, M.J., Tütüncü, R.H.: SDPT3: a Matlab software package for semidefinite programming, v. 1.3. Optim. Meth. Soft. 11(1–4), 545–581 (1999)
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Fampa, M., Lee, J. (2022). An Outer-Approximation Algorithm for Maximum-Entropy Sampling. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_10
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