Optimization of Utility Functions in an Admissible Space of Higher Dimension

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Author(s): German Almanza (University Autonomous of Juarez City, Mexico), Victor M. Carrillo (University Autonomous of Juarez City, Mexico)and Cely C. Ronquillo (University Autonomous of Juarez City, Mexico)
Copyright: 2016
Pages: 12
Source title: Handbook of Research on Military, Aeronautical, and Maritime Logistics and Operations
Source Author(s)/Editor(s): Alberto Ochoa-Zezzatti (Juarez City University, Mexico), Jöns Sánchez (Consejo Nacional De Ciencie Y Tecnologia (CONACYT), Mexico), Miguel Gastón Cedillo-Campos (Transportation Systems and Logistics National Laboratory, Mexican Institute of Transportation, Mexico)and Margain de Lourdes (Polytechnic University of Aguascalientes, Mexico)
DOI: 10.4018/978-1-4666-9779-9.ch006

Keywords: Business & Management / Business Science Reference / Management Science / Operations and Service Management

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Abstract

S. Smale published a paper where announce a theorem which optimize a several utility functions at once (cf. Smale, 1975) using Morse Theory, this is a very abstract subject that require high skills in Differential Topology and Algebraic Topology. Our goal in this paper is announce the same theorems in terms of Calculus of Manifolds and Linear Algebra, those subjects are more reachable to engineers and economists whom are concern with maximizing functions in several variables. Moreover, the elements involved in our theorems are accessible to graduate students, also we putting forward the results we consider economically relevant.

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Optimization of Utility Functions in an Admissible Space of Higher Dimension

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