Fundamentals of Optimization Theory
– Core concepts, problem types, and mathematical foundations.
Convex Optimization
– Theory, properties, and importance in practical applications.
Constrained and Unconstrained Optimization
– Analytical methods for problems with and without constraints.
Duality and Optimality Conditions
– Lagrangian duality, KKT conditions, and economic interpretations.
Linear and Nonlinear Programming
– Classical methods like simplex and modern approaches for nonlinear problems.
Numerical Optimization Algorithms
– Gradient-based, Newton-type, and iterative solution techniques.
Global Optimization and Metaheuristics
– Techniques for non-convex and complex optimization landscapes.
Stochastic, Robust, and Online Optimization
– Approaches for handling uncertainty, variability, and streaming data.
Optimization in Machine Learning and Data Science
– Loss minimization, regularization, and algorithm training.
Modeling and Solving Real-World Problems
– Using software tools (e.g., CVXPY, Pyomo, Gurobi) for practical applications.
