Trying to learn math from Wikipedia is like trying to learn English from the dictionary.
As far as the subject matter goes, a convex function can just be thought of as a function with a global maximum/minimum and no other local maximum/minimum. I.E. The derivative is zero in only one place which is the global max/min. These functions can then be easily optimized by taking their derivatives and finding the zero. It is a really nice way to optimize a problem.
...a convex function can just be thought of as a function with a global maximum/minimum and no other local maximum/minimum.
This is false. The convex function exp(x) has no global max or min. The function f(x,y)=x^2 has infinitely many global minima.
The nice thing about convex functions is that the set of places where they achieve a minimum is a convex set: the empty set for exp(x) and the line x=0 for f(x,y)=x^2.
No, in this case, a convex function is one where you can draw a straight line between any two points on its graph and not have the line intersect the graph at a third point.
I have about 5 years of informal/independent mathematical study and routinely use Wikipedia to crack fields open. I usually skim the intro then head straight to the references.
Once I have a vague idea of what it is, I drill down MathWorld using the new keywords.
Comments
Trying to learn math from Wikipedia is like trying to learn English from the dictionary.
As far as the subject matter goes, a convex function can just be thought of as a function with a global maximum/minimum and no other local maximum/minimum. I.E. The derivative is zero in only one place which is the global max/min. These functions can then be easily optimized by taking their derivatives and finding the zero. It is a really nice way to optimize a problem.
...a convex function can just be thought of as a function with a global maximum/minimum and no other local maximum/minimum.
This is false. The convex function exp(x) has no global max or min. The function f(x,y)=x^2 has infinitely many global minima.
The nice thing about convex functions is that the set of places where they achieve a minimum is a convex set: the empty set for exp(x) and the line x=0 for f(x,y)=x^2.
No, in this case, a convex function is one where you can draw a straight line between any two points on its graph and not have the line intersect the graph at a third point.
You are not contradicting what fgimenez said, its the same condition stated differently.
edit: if two statements are not essentially same (and I am wrong), could you please explain it.
The logarithm function is convex by this definition but has no maximum/minimum point and never has 0 derivative.
I have about 5 years of informal/independent mathematical study and routinely use Wikipedia to crack fields open. I usually skim the intro then head straight to the references.
Once I have a vague idea of what it is, I drill down MathWorld using the new keywords.