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 can be a local minimum.

Can you give me a real-world example of local minima?

Sure! In machine learning, local minima can occur during the training of a neural network, where the model finds a solution that is better than nearby solutions but not the best possible solution.

How do local minima affect optimization algorithms?

Local minima can trap optimization algorithms, preventing them from finding the global minimum. Techniques like simulated annealing or using momentum can help escape these traps.

What methods can be used to avoid local minima?

Methods like gradient descent with momentum, random restarts, or using evolutionary algorithms can help avoid getting stuck in local minima.