海塞矩阵和函数凸性

pingguagain 发表于 2014-10-20 11:11
The Hessian of f=xy is
0 1
1 0

I am making a programming recently.sone constraints of the model contain conbination of x(i)*y(i),i=1,2..n.
SO how to make those constraints convex? could you give me some useful suggestions for it is very important for my work.thank you.

pingguagain 发表于 2014-10-20 11:11
The Hessian of f=xy is
0 1
1 0

[x,y]=meshgrid(-1:0.1:1,-1:0.1:1);
z=x.*y;
contour(x,y,z,'g--')
Run these code on MAtLAB,you can see the area where x,y>0 is convex.I was confused.

【炊烟】 发表于 2014-10-20 12:13
I am making a programming recently.sone constraints of the model contain conbination of x(i)*y(i), ...

Convex function and convex set are two different concepts although there is some connection between them. For the relationship, read Chapter 6 of Dixit's book, Optimization in Economic Theory. Function f=xy is neither convex nor concave when x>0,y>0. However, the set {(x,y)|x>0,y>0, and xy>0} is convex.

pingguagain 发表于 2014-10-20 21:04
Convex function and convex set are two different concepts although there is some connection betwee ...

THANK YOU for your  great enthusiasm.I want to make sure that whether the feasible zone of constraint sum(i,x(i)*y(i))>0,(x(i),y(i)>0) is convex.