Class 1



  1. What is an Algorithm?
    1. Illustration of a trust region algorithm for unconstrained minimization.
    2. Illustration using Basic Lagrange Multipliers.
  2. Introduction to Nonlinear Programming
    1. Mathematical Formulation: example, level sets
    2. Definitions: local and global optima
    3. Definitions: convexity
  3. Fundamentals of Unconstrained Optimization (Recognizing Solutions)
    1. Definitions: gradient, Hessian, Taylor's Theorem, order notation (big and little O)
    2. directional derivative, curvature, linear model, direction of steepest descent
    3. first and second order necessary optimality conditions
    4. second order sufficient optimality conditions