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

2021 ◽  
Author(s):  
F. Flores-Bazán ◽  
Y. García ◽  
N. Hadjisavvas
Keyword(s):  
Quasiconvex Functions ◽  
Quasiconvex Optimization

scholarly journals Quasiconvexity and Density Topology

2014 ◽  
Vol 57 (1) ◽  
pp. 178-187 ◽  
Author(s):  
Patrick J. Rabier
Keyword(s):  
Open Subset ◽  
Measure Zero ◽  
Quasiconvex Functions ◽  
Density Topology ◽  
Approximate Continuity ◽  
The Common

AbstractWe prove that if f : ℝN → ℝ̄ is quasiconvex and U ⊂ ℝN is open in the density topology, then supU ƒ = ess supU f ; while infU ƒ = ess supU ƒ if and only if the equality holds when U = RN: The first (second) property is typical of lsc (usc) functions, and, even when U is an ordinary open subset, there seems to be no record that they both hold for all quasiconvex functions.This property ensures that the pointwise extrema of f on any nonempty density open subset can be arbitrarily closely approximated by values of ƒ achieved on “large” subsets, which may be of relevance in a variety of situations. To support this claim, we use it to characterize the common points of continuity, or approximate continuity, of two quasiconvex functions that coincide away from a set of measure zero.

Evenly Quasiconvex Functions

2020 ◽  
pp. 101-122
Author(s):  
María D. Fajardo ◽  
Miguel A. Goberna ◽  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Quasiconvex Functions

Second-order characterizations of C1-smooth robustly quasiconvex functions

2018 ◽  
Vol 46 (6) ◽  
pp. 568-572 ◽  
Author(s):  
Pham Duy Khanh ◽  
Vo Thanh Phat
Keyword(s):  
Second Order ◽  
Quasiconvex Functions

On Quasiconvex Functions on Time Scales

2018 ◽  
Vol 8 (4) ◽  
pp. 1-10
Author(s):  
Gregory l-Kpeng ◽  
Mohammed Iddrisu
Keyword(s):  
Time Scales ◽  
Quasiconvex Functions

Additively decomposed quasiconvex functions

1986 ◽  
Vol 35 (1) ◽  
pp. 42-57 ◽  
Author(s):  
J. -P. Crouzeix ◽  
P. O. Lindberg
Keyword(s):  
Quasiconvex Functions

Semicontinuity and Quasiconvex Functions

1997 ◽  
Vol 94 (3) ◽  
pp. 715-726 ◽  
Author(s):  
R. N. Mukherjee ◽  
L. V. Reddy
Keyword(s):  
Quasiconvex Functions
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