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Quasiconvexity of sum of quasiconvex functions

open access: yesQuasiconvexity of sum of quasiconvex functions
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Duality theorems for quasiconvex programming with a reverse quasiconvex constraint

open access: yesDuality theorems for quasiconvex programming with a reverse quasiconvex constraint
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Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences

2021
We 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, 2020
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Suliman Al-Homidan, Loai Shaalan
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Two Characterizations of Quasiconvexity

open access: yesJournal of Optimization Theory and Applications
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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Quasiconvex Sets

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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Characterizing quasiconvexity of the pointwise infimum of a family of arbitrary translations of quasiconvex functions, with applications to sums and quasiconvex optimization

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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Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions

Journal of Optimization Theory and Applications, 1999
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Daniilidis, A., Hadjisavvas, N.
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