Analytical representation of concave and quasiconcave homogeneous functions. (3rd April 2017)

• Record Type: Journal Article
• Authors: Gorbunov, V. K.
• Is Part Of: Optimization. Volume 66:Number 4(2017)
• Page Start: 507
• Page End: 519
• Publication Date: 2017-04-03
• Subjects: Homogeneous -- concave and quasiconcave functions -- superlinear functions -- homogenizing -- Fenchel–Rockafellar representation -- utility and production functions; 26B25 -- 26B40 -- 90C56 -- 91B38 -- 91B42; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1278000
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The formula which implements bijection between the class of concave linearly homogeneous functions defined on the nonnegative orthant of an arithmetic space and the simpler class of concave functions defined on the standard (probabilistic) simplex is presented. Two generalizations of this formula for analytical representation of quasiconcave homogeneous function are also proposed. These formulas particularly extend opportunities of modelling production objects and consumption.