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Conjugacy in quasi-convex programming
Mathematical Programming, 1984One introduces a conjugacy relation and a subdifferential on the class of functions \(g:R^ n\to\bar R.\) It is shown that \(g^{**}=g\) iff g is proper (i.e. \(g(0)=\sup g),\) homogeneous of degree zero and evenly quasi- convex. As noted by the authors, the above notions are much related to the ones introduced by \textit{J. P. Crouzeix} [Math. Oper. Res.
Ury Passy, Eliezer Z. Prisman
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Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus [PDF]
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The familiar Fenchel-Moreau-Rockafellar duality scheme deduced from a conjugation is shown to be applicable to quasi-convex problems. Here quasi-affine functions take the place of affine functions. The links with other quasi-convex dualities are examined.
Jean-Paul Penot, Michel Volle
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A Review of Quasi-Convex Functions
Operations Research, 1971Many theorems involving convex functions have appeared in the literature since the pioneering work of Jensen. Recently some results have been obtained for a larger class of functions: quasi-convex. This review summarizes in condensed form results known to date, providing some refinements to gain further generality.
Harvey J. Greenberg +1 more
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On Quasi-Convexity of the Cost Function
The Scandinavian Journal of Economics, 1987For the study of duality of the cost indirect output correspondence, one needs to know when the cost function is quasi-convex in outputs. This paper gives a necessary and sufficient condition for quasi-convexity in outputs, under homotheticity of the input correspondence.
Rolf Färe, Ulla Lehmijoki, Rolf Fare
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Minimization of quasi-convex symmetric and of discretely quasi-convex symmetric functions
Optimization, 1996The main results, given in Section 3, deal with the effective computation of a minimum point x ∗ of a discretely quasi-convex symmetric function f In particular, an explicit formula for x ∗ is given if f is to be minimized under a linear symmetric constraint.
A. Hinderer, M. Stieglitz
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