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Quasiconvexity of sum of quasiconvex functions

Quasiconvexity of sum of quasiconvex functions
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Approximation of quasiconvex functions by neatly quasiconvex functions

Optimization Letters, 2020
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Suliman Al-Homidan, Loai Shaalan, Al-Homidan Suliman   +2 more
exaly   +3 more sources

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 ...
N Hadjisavvas, Fabian Flores-Bazán
exaly   +3 more sources

Is every radiant function the sum of quasiconvex functions?

Mathematical Methods of Operations Research, 2004
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Alberto Zaffaroni
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Functions Which Are Quasiconvex under Linear Perturbations

SIAM Journal on Optimization, 2012
A quasiconvex function is a function whose sublevel sets are convex. A function which is quasiconvex under every (possibly large) linear perturbation is, by definition, a convex function. In this well-written paper, motivated by applications in partial differential equations and optimal control, the authors study functions which are robustly ...
E N Barron
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Level Function Method for Quasiconvex Programming

Journal of Optimization Theory and Applications, 2001
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Minimizing the difference of two quasiconvex functions

Optimization Letters, 2019
The paper considers the difference of a quasiconvex (DQC) optimization problem in the form \[ \begin{cases} \inf f(x)-g(x)\\ \text{subject to}: x\in X, \end{cases}\tag{P} \] where \(X\) is a Banach space and \( f, g: X\rightarrow \overline{\mathbb{R}} = [-\infty, +\infty ] \) are quasiconvex functions.
Stephan Dempe, Dempe S, N Gadhi
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Semicontinuity and Quasiconvex Functions

Journal of Optimization Theory and Applications, 1997
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Mukherjee, R. N., Reddy, L. V.
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An Appropriate Subdifferential for Quasiconvex Functions

SIAM Journal on Optimization, 2002
The authors introduce a concept of subdifferential that is well adapted to the class of lower-semicontinuous quasiconvex functions. Several interesting properties and calculus rules are established. A related reference is [\textit{J. E. Martínez-Legaz} and \textit{J. E. Sach}, J. Convex Anal. 6, 1-11 (1999; Zbl 0942.49020)].
Aris Daniilidis, Nicolas Hadjisavvas, Juan Enrique Martínez-Legaz   +2 more
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