Optimization algorithms are methods used to minimize or maximize an objective function—typically a loss function in machine learning—by adjusting model parameters. They are central to training processes, especially in deep learning, where models are optimized over high-dimensional, non-convex spaces.

Basic methods include Gradient Descent, which updates parameters in the direction of the negative gradient, and its variants like Stochastic Gradient Descent (SGD), which uses mini-batches for faster, more scalable training. More advanced algorithms adapt learning rates or use momentum to accelerate convergence and improve stability.

Popular optimizers include:

• SGD with Momentum: Adds a velocity term to smooth updates.
• Adam: Combines momentum with adaptive learning rates per parameter.
• RMSprop: Adapts learning rates based on a moving average of squared gradients.
• Adagrad: Scales learning rates based on past gradient magnitudes.

Choice of optimizer affects convergence speed, generalization, and training stability. There’s no one-size-fits-all; tuning often depends on the model, data, and task.