Calculating Extremes Using Gradient Descent Method

When using gradient descent to calculate extremes, the algorithm typically converges to local minima. However, by implementing specific strategies, we can expand the search scope to locate global minima. One effective approach is learning rate decay, which gradually reduces the step size during optimization. This allows finer exploration near potential global minima and can be implemented in code by dynamically adjusting the learning rate parameter using functions like exponential decay or step-based reduction schedules. Another strategy involves stochastic gradient descent (SGD), which randomly selects samples during each iteration. This introduces noise into the optimization process, helping the algorithm escape local minima and better explore the solution space. In code implementations, SGD can be achieved by shuffling training data and processing mini-batches. Regardless of the chosen strategy, these methods maintain computational efficiency while improving the likelihood of finding global minima through careful parameter tuning and algorithmic enhancements.