Class 4



  1. Nonlinear Equations
    1. Newton's Method, derivation using linearization, WITH PROOF, convergence rate, Inexact Newton method, merit functions
    2. Continuation (Homotopy) methods, (general outline only)
  2. Theory of Constrained Optimization,
    1. Definitions: constrained program, feasible set Omega, tangent cone of Omega at x, polar cone (dual cone).
    2. Geometric necessary conditions of optimality (extension of Fermat's theorem) for min f(x) x in Omega
    3. Geometric characterization of optimality for the convex case, min f(x) x in Omega , where f convex function and Omega convex set
    4. Definitions: local vs global minimum, smoothing problems by adding constraints, active constraints,