Read More
Date: 12-5-2021
![]()
Date: 8-5-2021
![]()
Date: 3-6-2021
![]() |
Given a subset and a real function
which is Gâteaux differentiable at a point
,
is said to be pseudoconvex at
if
![]() |
Here, denotes the usual gradient of
.
The term pseudoconvex is used to describe the fact that such functions share many properties of convex functions, particularly with regards to derivative properties and finding local extrema. Note, however, that pseudoconvexity is strictly weaker than convexity as every convex function is pseudoconvex though one easily checks that is pseudoconvex and non-convex.
Similarly, every pseudoconvex function is quasi-convex, though the function is quasi-convex and not pseudoconvex.
A function for which
is pseudoconvex is said to be pseudoconcave.
REFERENCES:
Borwein, J. and Lewis, A. Convex Analysis and Nonlinear Optimization: Theory and Examples. New York: Springer Science+Business Media, 2006.
|
|
إدارة الغذاء والدواء الأميركية تقرّ عقارا جديدا للألزهايمر
|
|
|
|
|
شراء وقود الطائرات المستدام.. "الدفع" من جيب المسافر
|
|
|
|
|
العتبة العبّاسيّة: البحوث الّتي نوقشت في أسبوع الإمامة استطاعت أن تثري المشهد الثّقافي
|
|
|