MATH285 Optimization

The course gives an introduction to the field of optimization, where we will cover four main topics:

• Basic concepts
  • Convexity
  • Lines and hyperplanes
  • Taylor’s theorem
• Unconstrained optimization
  • Optimality conditions
  • Search methods (Gradient methods and Newton’s method)
• Linear programming
  • Standard form
  • Inequalities and slack variables
  • Simplex method
  • Duality
• Non-linear constrained optimization
  • Optimality conditions
  • Convex optimization
  • Solution algorithms

The students are to learn the basic theory of optimization. More specifically, they are expected to:

• Explain basic concepts and results from the theory
• Solve simple problems analytically
• Recognize different types of optimization problems
• Be able to implement a set of known algorithms in order to solve optimization problems numerically