AIExplainer
Deep Learning Mathematics Intermediate 2 min read

What is convex function?

A mathematical function where the line segment connecting any two points on the function's graph lies above or on the graph

A convex function is a type of mathematical function that has a specific shape, where the curve is always bending upwards. This means that if you draw a line between any two points on the curve, the line will always be above or on the curve, never below it.

Imagine a bowl-shaped curve, where a marble rolled between any two points on the curve would always follow a path that is above or on the curve, never below it. This is similar to how a convex function behaves.

A simple example of a convex function is the cost of producing a certain number of units of a product. As the number of units increases, the cost may increase at an increasing rate, resulting in a convex curve.

Convex functions are used in optimization problems, where the goal is to find the minimum or maximum of a function. They are also used in machine learning and artificial intelligence to model complex relationships between variables.

One common misconception is that all convex functions are linear, but this is not the case. Convex functions can have a variety of shapes, as long as they satisfy the convexity property.

The concept of convex functions has been around for centuries, but it wasn't until the 20th century that they became a fundamental tool in optimization and machine learning.

convex curve concave down function

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