Uniform quasi-concavity in probabilistic constrained stochastic programming

Authors:
AndráS PréKopa;Kunikazu Yoda;Munevver Mine Subasi
Affiliations:
RUTCOR, Rutgers Center for Operations Research, 640 Bartholomew Rd., Piscataway, NJ 08854, United States;RUTCOR, Rutgers Center for Operations Research, 640 Bartholomew Rd., Piscataway, NJ 08854, United States;Florida Institute of Technology, Department of Mathematical Sciences, 150 W. University Blvd., Melbourne, FL 32901, United States
Venue:
Operations Research Letters
Year:
2011

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Abstract

A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi-concavity of the constraining function needed for the convexity of the problem is ensured if the factors of the function are uniformly quasi-concave. A necessary and sufficient condition is given for that property to hold. It is also shown, through numerical examples, that such a special problem still has practical application in optimal portfolio construction.