Overview

We want to find the best solution under constraints. Optimization problems arise across virtually all areas of science ranging from cognitive science to machine learning. Though Linear Programming (optimization) has achieved remarkable success in practice, many important optimization problems involve nonlinear objectives or constraints, for which analytical solutions are usually unavailable.

This course focuses on the computational methods for solving such nonlinear optimization problems and the theory behind them, bridging mathematical rigor with practical algorithms. 

Lectures

We basically cover the textbook: Nonlinear Programming by Dimitri Bertsekas, and beyond. Topics include:

1. Unconstrained Optimization

2. Constrained Optimization

   • Convex Optimization

   • Lagrange Multiplier

   • Duality Theory

3. Dynamic Programming

Group Project

Beyond classroom topics, students will tackle real-world problems with their group members by implementing the computational methods or extend their theoretical knowledge. Groups are expected to present their results in the final "minisymposium."