Semi-infinite probabilistic optimization: first-order stochastic dominance constrain

References

• Arjas , E and Gasbarra , D . 1996 . Bayesian inference of survival probabilities, under stochastic ordering constraints . J. Amer. Statist. Assoc. , 91 : 1101 – 1109 .
   Web of Science ®Google Scholar
• Birkhoff , G . 2000 . Tres obsevaciones sobre el algebra lineal . Univ. Nac. Tucumán Rev. Ser. A , 5 : 147 – 151 .
   Google Scholar
• Bonnans JF Shapiro A 2000 Perturbation Analysis of Optimization Problems, Springer-Verlag New York
   Google Scholar
• Borell , C . 1975 . Convex set functions in d-Space . Periodica Mathematica Hungarica , 6 : 111 – 136 .
   Google Scholar
• Brascamp , HJ and Lieb , EH . 1976 . On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log-concave functions and with an application to the diffusion equation . Journal of Functional Analysis , 22 : 366 – 389 .
   Web of Science ®Google Scholar
• Dentcheva , D and Ruszczyński , A . 2003 . Optimization under linear stochastic dominance . Comptes Rendus de l'Academie Bulgare des Sciences , 56 ( 6 ) : 5 – 10 .
   Google Scholar
• Dentcheva , D and Ruszczyński , A . 2003 . Optimization under nonlinear stochastic dominance . Comptes Rendus de l'Academie Bulgare des Sciences , 56 ( 7 ) : 17 – 22 .
   Google Scholar
• Dentcheva , D and Ruszczyński , A . 2003 . Optimization with stochastic dominance constraints . SIAM Journal on Optimization , 14 : 548 – 566 .
   Web of Science ®Google Scholar
• Dentcheva , D and Ruszczyński , A . 2004 . Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints . Mathematical Programming , 99 : 329 – 350 .
   Web of Science ®Google Scholar
• Ya. Dubovitskii , A and Milyutin , AA . 1965 . Extremal problems in the presence of constrains . Zhurnal Vych. Mat. i Mat. Fiz. , 5 : 395 – 453 .
   Google Scholar
• Dudley RM 2002 Real Analysis and Probability, Cambridge Univ. Press Cambridge
   Google Scholar
• Fishburn PC 1970 Utility Theory for Decision Making, Wiley New York
   Google Scholar
• Gangnon , RE and King , WN . 2002 . Minimum distance estimation of the distribution functions of stochastically ordered random variables . Journal of the Royal Statistical Society: Series C (Applied Statistics) , 51 ( 4 ) : 485 – 498 .
   Web of Science ®Google Scholar
• Hadar , J and Russell , W . 1969 . Rules for ordering uncertain prospects . The American Economic Review , 59 : 25 – 34 .
   Web of Science ®Google Scholar
• Hardy GH Littlewood JE Pólya G 1934 Inequalities, Cambridge University Press Cambridge MA
   Google Scholar
• Klatte , D and Henrion , R . 1998 . Regularity and stability in nonlinear semi-infinite optimization . Nonconvex optimization and Applications , 25 : 69 – 102 .
   Google Scholar
• Kurcyusz , S and Zowe , J . 1979 . Regularity and stability for the mathematical programming problem in Banach spaces . Appl. Math. Optim. , 5 : 49 – 62 .
   Web of Science ®Google Scholar
• Lehmann , E . 1947 . Ordered families of distributions . Annals of Mathematical Statistics , 26 : 399 – 419 .
   Google Scholar
• Mann , HB and Whitney , DR . 1947 . On a test of whether one of two random variables is stochastically larger than the other . Ann. Math. Statistics , 18 : 50 – 60 .
   Google Scholar
• Marshall AW Olkin I 1979 Inequalities: Theory of Majorization and Its Applications, Academic Press San Diego
   Google Scholar
• Mosler K Scarsini M 1991 (Eds.) Stochastic Orders and Decision Under Risk, Institute of Mathematical Statistics Hayward California
   Google Scholar
• Müller A Stoyan D 2002 Comparison Methods for Stochastic Models and Risks, John Wiley & Sons Chichester
   Google Scholar
• Ogryczak , W and Ruszczyński , A . 2001 . On consistency of stochastic dominance and mean – semideviation models . Mathematical Programming , 89 : 217 – 232 .
   Web of Science ®Google Scholar
• Prékopa A 1970 On probabilistic constrained programming Proceedings of the Princeton Symposium on Mathematical Programming 113 138 Princeton University Press Princeton
   Google Scholar
• Prékopa , A . 1971 . Logarithmic concave functions with applications to stochastic programming . Acta Sci. Math. (Szeged) , 32 : 301 – 316 .
   Web of Science ®Google Scholar
• Prékopa A 1995 Stochastic Programming, Kluwer Dordrecht, Boston
   Google Scholar
• Quirk , JP and Saposnik , R . 1962 . Admissibility and measurable utility functions . Review of Economic Studies , 29 : 140 – 146 .
   Web of Science ®Google Scholar
• Robinson , SM . 1976 . Stability theory for systems of inequalities. II: differentiable nonlinear systems . SIAM J. Numer. Anal. , 13 : 497 – 513 .
   Web of Science ®Google Scholar
• Rockafellar RT Wets RJ-B 1998 Variational Analysis, Springer-Verlag Berlin
   Google Scholar
• Ruszczyński A Shapiro A 2003 (Eds.) Stochastic Programming, Elsevier Amsterdam
   Google Scholar
• Strassen , V . 1965 . The existence of probability measures with given marginals . Annals of Mathematical Statistics , 38 : 423 – 439 .
   Google Scholar
• Szekli R 1995 Stochastic Ordering and Dependence in Applied Probability, Springer-Verlag New York
   Google Scholar