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Cardinality of upper average and its application to network optimization. (English) Zbl 1391.90407

90C05 Linear programming
90C35 Programming involving graphs or networks
90C25 Convex programming
90C11 Mixed integer programming
90C90 Applications of mathematical programming
Full Text: DOI
[1] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications, 1st ed., Pearson, London, 1993. · Zbl 1201.90001
[2] D. P. Bertsekas, Network Optimization: Continuous and Discrete Models, Athena Scientific, Belmont, MA, 1998. · Zbl 0997.90505
[3] D. Bienstock, M. Chertkov, and S. Harnett, Chance-constrained optimal power flow: Risk-aware network control under uncertainty, SIAM Rev., 56 (2014), pp. 461–495. · Zbl 1301.93095
[4] D. Bienstock and S. Mattia, Using mixed-integer programming to solve power grid blackout problems, Discrete Optim., 4 (2007), pp. 115–141. · Zbl 1173.90335
[5] S. Binato, M. V. F. Pereira, and S. Granville, A new Benders decomposition approach to solve power transmission network design problems, IEEE Trans. Power Syst., 16 (2001), pp. 235–240.
[6] D. Bertsimas, D. Pachamanova, and M. Sim, Robust linear optimization under general norms, Oper. Res. Lett., 32 (2004), pp. 510–516. · Zbl 1054.90046
[7] J. R. Davis and S. Uryasev, Analysis of tropical storm damage using buffered probability of exceedance, Nat. Hazards, 83 (2016), 465–483.
[8] H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, de Gruyter Textbook, 3rd ed., de Gruyter, Berlin, 2011.
[9] A. Mafusalov and S. Uryasev, Buffered Probability of Exceedance: Mathematical Properties and Optimization Algorithms, Research report 2014-1, University of Florida, Gainesville, FL, 2015. · Zbl 1395.90191
[10] A. Mafusalov and S. Uryasev, Conditional Value-at-Risk (CVaR) Norm: Stochastic Case, Research report 2013-5, University of Florida, Gainesville, FL, 2014. · Zbl 1346.91266
[11] T. L. Magnanti and R. T. Wong, Network design and transportation planning: Models and algorithms, Transp. Sci., 18 (1984), pp. 1–55.
[12] M. Norton and S. Uryasev, Maximization of AUC and Buffered AUC in Binary Classification, Research report 2014-2, University of Florida, Gainesville, FL, 2014.
[13] F. Ordón͂ez and J. Zhao, Robust capacity expansion of network flows, Networks, 50 (2007), pp. 136–145.
[14] K. Pavlikov and S. Uryasev, CVaR norm and applications in optimization, Optim. Lett., 8 (2014), pp. 1999–2020. · Zbl 1332.90280
[15] R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, J. Risk, 2 (2000), pp. 21–41.
[16] R. T. Rockafellar, Safeguarding strategies in risky optimization, Presentation, International Workshop on Engineering Risk Control and Optimization, University of Florida, Gainesville, FL, 2009.
[17] R. T. Rockafellar and J. O. Royset, On buffered failure probability in design and optimization of structures, Reliab. Engin. Syst. Safety, 95 (2010), pp. 499–510.
[18] S. Uryasev, Buffered Probability of Exceedance and Buffered Service Level: Definitions and Properties, Research report 2014-3, University of Florida, Gainesville, FL, 2014.
[19] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybernet., 18 (1988), pp. 183–190. · Zbl 0637.90057
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