[1] Delage, E., Ye, Y.:Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3), 595-612(2010)
[2] Goh, J., Sim, M.:Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4-part-1), 902-917(2010)
[3] Calafiore, G.C.:Ambiguous risk measures and optimal robust portfolios. SIAM J. Optim. 18(3), 853-877(2007)
[4] Klabjan, D., Simchi-Levi, D., Song, M.:Robust stochastic lot-sizing by means of histograms. Prod. Oper. Manag. 22(3), 691-710(2013)
[5] Ben-Tal, A., Den Hertog, D., De Waegenaere, A., Melenberg, B., Rennen, G.:Robust solutions of optimization problems affected by uncertain probabilities. Manag. Sci. 59(2), 341-357(2013)
[6] Ben-Tal, A., Bertsimas, D., Brown, D.:A soft robust model for optimization under ambiguity. Oper. Res. 58(4), 1220-1234(2010)
[7] Carlsson, J.G., Devulapalli, R.:Dividing a territory among several facilities. INFORMS J. Comput. 25(4), 730-742(2012). Accessed 1 Apr 2018
[8] Jaynes, E.T.:Information theory and statistical mechanics. Phys. Rev. 104(4), 620-630(1957)
[9] Hyndman, Rob J.:Computing and graphing highest density regions. Am. Stat. 50(2), 120-126(1996)
[10] Goffin, J.-L., Vial, J.-P.:Convex nondifferentiable optimization:a survey focused on the analytic center cutting plane method. Optim Methods Softw. 17(5), 805-867(2002)
[11] Calafiore, G.C., El Ghaoui, L.:On distributionally robust chance-constrained linear programs. J. Optim. Theory Appl. 130(1), 1-22(2006)
[12] Pavone, M., Savla, K., Frazzoli, E.:Sharing the load. IEEE Robot. Autom. Mag. 16, 52-61(2009)
[13] Xie, W., Ouyang, Y.:Optimal layout of transshipment facility locations on an infinite homogeneous plane. Transp. Res. Part B Methodol. 75, 74-88(2015)
[14] Daganzo, C.:Logistics Systems Analysis. Springer, Berlin (2005)
[15] Halverson, N.:Google claims right to post photos from private land. The Press Democrat (2008)
[16] Popescu, I.:Robust mean-covariance solutions for stochastic optimization. Oper. Res. 55(1), 98-112(2007)
[17] Zymler, S., Kuhn, D., Rustem, B.:Distributionally robust joint chance constraints with second-order moment information. Math. Program. 137(1-2), 167-198(2013)
[18] Chen, X., Sim, M., Sun, P.:A robust optimization perspective on stochastic programming. Oper. Res. 55(6), 1058-1071(2007)
[19] Carlsson, J.G., Delage, E.:Robust partitioning for stochastic multivehicle routing. Oper. Res. 61(3), 727-744(2013)
[20] Caillerie, C., Chazal, F., Dedecker, J., Michel, B.:Deconvolution for the Wasserstein metric and geometric inference. In Geometric Science of Information. Springer, pp. 561-568(2013)
[21] Irpino, A., Verde, R.:A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data. In Data Science and Classification. Springer, pp. 185-192(2006)
[22] Pampalk, E., Flexer, A., Widmer, G., et al.:Improvements of audio-based music similarity and genre classification. In ISMIR, vol. 5, pp. 634-637. London, UK (2005)
[23] Rubner, Y., Tomasi, C., Guibas, L.J.:The earth mover's distance as a metric for image retrieval. Int. J. Comput. Vis. 40(2), 99-121(2000)
[24] Erdoǧan, E., Iyengar, G.:Ambiguous chance constrained problems and robust optimization. Math. Program. 107(1-2), 37-61(2006)
[25] Wozabal, D.:A framework for optimization under ambiguity. Ann. Oper. Res. 193(1), 21-47(2012)
[26] Wozabal, D.:Robustifying convex risk measures for linear portfolios:a nonparametric approach. Oper. Res. 62(6), 1302-1315(2014)
[27] Bertsimas, D., Gupta, V., Kallus, N.:Data-driven robust optimization. arXiv preprint arXiv:1401.0212(2013)
[28] Iyengar, G.N.:Robust dynamic programming. Math. Oper. Res. 30(2), 257-280(2005)
[29] Pflug, David Wozabal Georg:Ambiguity in portfolio selection. Quant. Finance 7, 435-442(2007)
[30] Carlsson, J.G., Behroozi, M., Mihic, K.:Wasserstein distance and the distributionally robust TSP. Oper. Res. 66(6), 1603-1624(2018)
[31] Kleywegt, A.J., Gao, R.:Distributionally robust stochastic optimization with Wasserstein distance. arXiv:1604.02199(2016)
[32] Esfahani, P.M., Kuhn, D.:Data-driven distributionally robust optimization using the Wasserstein metric:performance guarantees and tractable reformulations. arXiv:1505.05116(2015)
[33] Murthy, K., Blanchet, J., Kang, Y.:Robust Wasserstein profile inference and applications to machine learning. arXiv:1610.05627(2017)
[34] Luenberger, D.G.:Optimization by Vector Space Methods. Wiley, Hoboken (1968)
[35] Villani, C.:Topics in Optimal Transportation. AMS, Philadelphia (2003)
[36] Amari, S., Karakida, R., Oizumi, M.:Information geometry connecting Wasserstein distance and Kullback-Leibler divergence via the entropy-relaxed transportation problem. Information Geometry, pp. 1-25(2018)
[37] Royden, H.L., Fitzpatrick, P.:Real Analysis, vol. 32. Macmillan, New York (1988)
[38] Dunford, N., Schwartz, J.T.:Linear Operators Part I:General Theory, vol. 7. Interscience Publishers, New York (1958)
[39] Boyd, S.:Localization and cutting-plane methods. http://stanford.edu/class/ee364b/lectures/localization_methods_slides.pdf (2014)
[40] Canas, G., Rosasco, L.:Learning probability measures with respect to optimal transport metrics. In Advances in Neural Information Processing Systems, pp. 2492-2500(2012)
[41] Fournier, N., Guillin, A.:On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Relat. Fields 162(3-4), 707-738(2015)
[42] Villani, C.:Optimal Transport:Old and New, vol. 338. Springer, Berlin (2008)
[43] Bolley, F., Villani, C.:Weighted csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Annales de la Faculté des sciences de Toulouse:Mathématiques 14, 331-352(2005)
[44] Bolley, F., Guillin, A., Villani, C.:Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory Relat. Fields 137(3-4), 541-593(2007)
[45] Krantz, S.G., Parks, H.R.:Geometric Integration Theory. Cornerstones, Birkhäuser (2008) |
