caa a22 4500 475769422 CHVBK 20180406123615.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/PL00011393 doi (NATIONALLICENCE)springer-10.1007/PL00011393 Concavity and efficient points of discrete distributions in probabilistic programming [Elektronische Daten] [Darinka Dentcheva, András Prékopa, Andrzej Ruszczynski] Abstract. : We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples. Springer-Verlag Berlin Heidelberg, 2000 Key words: probabilistic programming - discrete distributions - generalized concavity - column generation Mathematics Subject Classification (1991): 90C15, 90C11, 65K05, 49M27 nationallicence Dentcheva Darinka Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA, and RUTCOR (Rutgers University Center for Operations Research), Piscataway, NJ 08854, USA, e-mail: darina@rutcor.rutgers.edu, US aut Prékopa András RUTCOR, e-mail: prekopa@rutcor.rutgers.edu, US aut Ruszczynski Andrzej RUTCOR and Department of Management Science and Information Systems, Rutgers University, Piscataway, NJ 08854, USA, e-mail: rusz@rutcor.rutgers.edu, US aut https://doi.org/10.1007/PL00011393 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00011393 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dentcheva Darinka Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA, and RUTCOR (Rutgers University Center for Operations Research), Piscataway, NJ 08854, USA, e-mail: darina@rutcor.rutgers.edu, US aut NATIONALLICENCE 700 1- Prékopa András RUTCOR, e-mail: prekopa@rutcor.rutgers.edu, US aut NATIONALLICENCE 700 1- Ruszczynski Andrzej RUTCOR and Department of Management Science and Information Systems, Rutgers University, Piscataway, NJ 08854, USA, e-mail: rusz@rutcor.rutgers.edu, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer