What are local minima in optimization?

What are local minima in optimization?

Local minima are points in a function where the value is lower than at nearby points, but not necessarily the lowest overall.

How do local minima affect optimization algorithms?

They can cause algorithms to get stuck, preventing them from finding the global minimum, which is the best solution.

Can you give an example of a function with local minima?

Sure! The function f(x) = x^4 - 3x^3 + 2 has local minima at certain points, even though it also has a global minimum.

What techniques can be used to avoid local minima?

Techniques like simulated annealing, genetic algorithms, and using momentum in gradient descent can help avoid local minima.