Table of Contents
- 1 What is an example of a convex function?
- 2 How do you show a function is convex?
- 3 What is convex and concave function?
- 4 Is sinusoidal function convex?
- 5 What is convex function in machine learning?
- 6 Is exp function convex?
- 7 What is the difference between concave and convex functions?
- 8 How do you prove a function is convex?
- 9 Is linear function convex or concave?
What is an example of a convex function?
Convex function on an interval. A function (in black) is convex if and only if the region above its graph (in green) is a convex set. A graph of the bivariate convex function x2 + xy + y2.
How do you show a function is convex?
A function f : Rn → R is convex if and only if the function g : R → R given by g(t) = f(x + ty) is convex (as a univariate function) for all x in domain of f and all y ∈ Rn. (The domain of g here is all t for which x + ty is in the domain of f.)
Is e x convex?
The function ex is differentiable, and its second derivative is ex > 0, so that it is (strictly) convex. Hence by a result in the text the set of points above its graph, {(x, y): y ≥ ex} is convex.
What is convex and concave function?
A function that has an increasing first derivative bends upwards and is known as a convex function. We also describe a concave function as a negative of a convex function. Instead of saying that a function is concave, we can also say that it is concave downwards because a concave function always bends downwards.
Is sinusoidal function convex?
sin is not convex. It can be proved easily.
Does Sinx have points of inflection?
Points of inflection on a graph are where the concavity of the graph changes. In this case, you’re looking for the inflection point of: f(x)=sinx+cosx on the interval of [0,2π] . The inflection point comes from where the second derivative is equal to 0.
What is convex function in machine learning?
Most of the cost functions in the case of neural networks would be non-convex. Thus you must test a function for convexity. A function f is said to be a convex function if the seconder-order derivative of that function is greater than or equal to 0. Condition for convex functions.
Is exp function convex?
The function f(x)=expx is strictly convex.
Is e x convex function?
The function ex is differentiable, and its second derivative is ex > 0, so that it is (strictly) convex. Hence by a result in the text the set of points above its graph, {(x, y): y ≥ ex} is convex. Convex: see the following figure.
What is the difference between concave and convex functions?
The major difference between concave and convex lenses lies in the fact that concave lenses are thicker at the edges and convex lenses are thicker in the middle. These distinctions in shape result in the differences in which light rays bend when striking the lenses.
How do you prove a function is convex?
There are many ways of proving that a function is convex: By definition. Construct it from known convex functions using composition rules that preserve convexity. Show that the Hessian is positive semi-definite (everywhere that you care about) Show that values of the function always lie above the tangent planes of the function.
Can you prove that this function is convex?
There are many ways of proving that a function is convex: Unless you know something about the properties of the function (e.g., whether it’s a quadratic polynomial, monotonic, etc), you can not experimentally determine whether a function is convex. You need to limit your question to a smaller subset of functions.
Is linear function convex or concave?
If in the whole range it is positive then it is convex if it is negative then it is concave, if it can be both positive and negative (for some sub-range) then it is neither convex nor concave. Linear functions (with second order derivative zero) are both convex and concave.