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.
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Communicated by F. Giannessi
Thanks are due to Professor F. Giannessi for correcting a number of details of thepresentation
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Islam, S.M.N., Craven, B. Some Extensions of Nonconvex Economic Modeling: Invexity, Quasimax, and New Stability Conditions. J Optim Theory Appl 125, 315–330 (2005). https://doi.org/10.1007/s10957-004-1840-1
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DOI: https://doi.org/10.1007/s10957-004-1840-1