What are some examples of local minima in optimization?

What are some examples of local minima in optimization?

Local minima are points where a function has a lower value than its neighboring points, but not necessarily the lowest overall. For example, in a simple quadratic function, the vertex is a local minimum.

Can you give me a real-world example?

Sure! In machine learning, when training a model, the loss function may have multiple local minima. The model might settle in one of these local minima instead of finding the global minimum, affecting its performance.

How can we avoid getting stuck in local minima?

Techniques like using momentum in gradient descent, employing simulated annealing, or using multiple initializations can help avoid local minima.

What is the difference between local minima and global minima?

A local minimum is a point that is lower than its immediate neighbors, while a global minimum is the lowest point in the entire function.