gradient methods

Gradient methods are techniques used in optimization to find the best solution by iteratively improving it. Imagine trying to descend a foggy mountain to reach the lowest point; gradient methods tell you which way to go downward based on the slope (gradient) of the terrain at your current position. By consistently moving opposite to the gradient, you get closer to the optimal solution, such as minimizing errors or costs. These methods are fundamental in machine learning and data fitting, helping computers learn patterns by efficiently adjusting parameters to improve performance.