Optimization is a cartography of extrema, a guide for the exploration of efficiency and efficacy. From the basic trails marked by gradient descent to the arcane paths revealed through linear programming, it dictates the most effective routes in algorithmic landscapes. ![[DALLE3_Optimization.png]] ## Concept Tree ### Basic 1. **Introduction to Optimization Problems** - Definition and examples - Objective functions and constraints 2. **Simple Methods** - Gradient Descent - Momentum - Nesterov's Accelerated Gradient ### Advanced 1. **Advanced Optimization Techniques** - Stochastic Gradient Descent (SGD) - Newton's Method - Conjugate Gradient Method - Adaptive learning rate methods (e.g., Adam, RMSProp) 2. **Understanding Optimization Landscapes** - Convex vs. non-convex functions - Saddle points and local minima ### Mastery 1. **Constrained Optimization** - Lagrange multipliers - Karush-Kuhn-Tucker (KKT) conditions - Quadratic programming 2. **Linear Programming** - Simplex method - Duality 3. **Role of Optimization in Machine Learning and AI** - Hyperparameter tuning - Model selection - Understanding training dynamics