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Quasiconvexity of sum of quasiconvex functions
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Duality theorems for quasiconvex programming with a reverse quasiconvex constraint
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Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences
2021We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are asymmetric distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as the limit case of scaled and skewed quasiconvex Jensen divergences, and report a simple closed-form formula which shows that ...
Frank Nielsen, Gaëtan Hadjeres
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Approximation of quasiconvex functions by neatly quasiconvex functions
Optimization Letters, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suliman Al-Homidan, Loai Shaalan
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Two Characterizations of Quasiconvexity
We present two characterisations of quasiconvexity for radially semicontinuous mappings defined on a convex subset of a real linear space. As applications, we obtain an extension of Sion's minimax theorem and two characterisations of quasiconvex risk measures.
Wlodzimierz Fechner +1 more
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Canadian Journal of Mathematics, 1950
Introduction. Let I be the closed real number interval: Any subset Δ of I containing at least one number interior to I, will be called a quasiconvexity generating set. To each quasiconvexity generating set Δ we associate as follows a generalized notion of convexity, here called quasiconvexity or Δ convexity.
Green, J. W., Gustin, W.
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Introduction. Let I be the closed real number interval: Any subset Δ of I containing at least one number interior to I, will be called a quasiconvexity generating set. To each quasiconvexity generating set Δ we associate as follows a generalized notion of convexity, here called quasiconvexity or Δ convexity.
Green, J. W., Gustin, W.
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Mathematical Programming, 2021
An essential goal of this paper is to find sufficient conditions or even characterizations for quasiconvex functions such that sum or minimum of two (or finitely many) such funtions are again quasiconvex. To do this, the authors use the connection between quasiconvex functions \(f\) and quasimonotone operators (think of \(\partial{f}\)), use a new ...
Fabián Flores Bazán +2 more
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An essential goal of this paper is to find sufficient conditions or even characterizations for quasiconvex functions such that sum or minimum of two (or finitely many) such funtions are again quasiconvex. To do this, the authors use the connection between quasiconvex functions \(f\) and quasimonotone operators (think of \(\partial{f}\)), use a new ...
Fabián Flores Bazán +2 more
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Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniilidis, A., Hadjisavvas, N.
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