Read More
Date: 4-8-2021
![]()
Date: 13-6-2021
![]()
Date: 21-6-2021
![]() |
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.
|
|
منها نحت القوام.. ازدياد إقبال الرجال على عمليات التجميل
|
|
|
|
|
دراسة: الذكاء الاصطناعي يتفوق على البشر في مراقبة القلب
|
|
|
|
|
هيئة الصحة والتعليم الطبي في العتبة الحسينية تحقق تقدما بارزا في تدريب الكوادر الطبية في العراق
|
|
|