Some Extensions of Nonconvex Economic Modeling: Invexity, Quasimax, and New Stability Conditions

S. M. N. Islam and B.D. Craven
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S. M. N. Islam: Victoria University
B.D. Craven: University of Melbourne

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 2, No 4, 315-330

Abstract: Abstract There are many applications in economics of nonlinear programming, usually under convexity assumptions. Some nonconvex models have also been discussed extensively in order to relax the restrictive assumption of convexity. The applicability can be extended considerably by further generalization to invexity and of maximum to quasimax. Some qualitatively different effects may occur with nonconvex models, such as nonunique optima at different objective levels and jumps in the consumption function, which have economic significance. This paper describes these effects and relates them to mathematical concepts.

Keywords: Optimal growth; optimal control; nonunique optimum; pseudoconcvave functions; invex functions; control jumps; quasimax (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1840-1

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