Convex & Concave

published on 10.11.2018

Convex Sets

Bir küme içerisinden seçilen her bir iki nokta için; bu iki nokta bir doğru ile birleştirildiğinde eğer bu doğru küme içerisinde kalıyorsa bu set convex settir.

Any two convex set that don’t touch each other(don’t intersect) can be seperated by a simple straight line.

Convex & Concave Functions

Seçilen herhangi iki nokta düz bir doğru ile birleştirildiğinde bu doğru fonksiyonun üzerinde kalıyorsa, fonksiyona convex fonksiyon denir. Altında kalıyorsa konkav fonksiyon denir.

f is convex if $f''(x)>0$

f is concave if $f''(x)<0$

Eğer fonksiyon, multivariable ise $f(x,y,z,…)$ gibi… Her bir değişken için ikinci kısmi türevine (second order partial derivative) bakılır ve Hessian matrisi oluşturulur.

You might be interested in:

Convex Optimization
LP and QP

Published on 10.11.2018 by Mert Bakır with commit db8d56a.

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