---

1. Introduction (Chapter 1)
   1. Mathematical Formulation: example, level sets
   2. Definitions: local and global optima
   3. Definitions: convexity
2. Fundamentals of Unconstrained Optimization (Chapter 2)
   1. Example of nonlinear least squares data fitting
   2. Definitions: gradient, Hessian, Taylor's Theorem

---

1. Fundamentals Unconstrained Opt. cont... (Chapter 2)
   1. 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

---

1. Overview of Algorithms
   1. Importance of convex functions and sets for global optima
   2. line search and trust region methods
      1. line search: steepest descent, Newton's method (scale invariance)

---

1. Line Search Methods (Chapter 3), of type
   x_k+1= x_k+ alpha_k p_k,
   where p_k is the search direction and alpha_k is the step length
   1. Step Length
      1. Wolfe conditions (geometric interpretations)
         
         sufficient decrease step is not too large curvature condition step is not too small
      2. Lemma 3.1 (existence of step lengths)
   2. Convergence of Line Search Methods
      1. Theorem 3.2 (cos theta geometric interpretation)

   ---

2. Theorem 3.7 (with proof! quadratic convergence of Newton's method near optimum.)

---

1. Nonlinear Equations
   1. Newton's Method, derivation using linearization, Theorem 11.2 WITH PROOF, convergence rate, Inexact Newton method, merit functions

---

1. Theory of Constrained Optimization, Chap. 12, cont...
   1. Definitions: local vs global minimum, smoothing problems by adding constraints, active constraints,

---

1. Theory of Constrained Optimization, Chap. 12, cont...
   (with basic convex analysis/duality added)
   1. Examples using KKT conditions
   2. Examples of duals of convex programs
   3. sensitivity interpretation of Lagrange multipliers for convex programs

---

1. Sequential Quadratic Programming
2. Basics of Interior-Point Methods