Nonlinear Optimization for Decision Making

1 Unit · Graduate

Theory and algorithms of nonlinear optimization as a bridge between deterministic linear models and data-driven decision making under uncertainty. This course covers convex and nonconvex modeling, first- and second-order optimality conditions, duality theory, and numerical methods including gradient-based, stochastic, Newton-type, and constrained optimization algorithms. Case studies from machine learning, finance, and engineering motivate the formulation and analysis of real-world nonlinear models. Students implement foundational solvers from first principles, construct more advanced solvers using generative-AI assisted development, and deploy these methods on applications such as nonlinear regression and classification, portfolio optimization, and parameter estimation in complex systems.