| Week | Dates | topics | Notes |
|---|---|---|---|
| Week 1 | Sept. 8 | Background; Optimization examples and applications | Including summaries of background in: linear algebra; calculus; analysis |
| Week 2 | Sept 13 - Sept 15 | Introduction to unconstrained minimization | Optimality conditions; first and second order models |
| Week 3 | Sept. 20 - Sept. 22 | Algorithms for unconstrained minimization | First order algorithms, Newton type algorithms |
| Week 4 | Sept. 27 - Sept. 29 | Trust Region Methods | Implementation, convergence results |
| Week 5 | Jan 30 - Feb 3 | Large scale unconstrained minimization | Conjugate gradient methods, exploiting sparsity, role of convexity |
| Week 6 | Oct. 4 - Oct. 6 | Introduction to constrained minimization | Various models, convexity |
| Week 7 | Oct. 18 - Oct. 20 | Optimality conditions | Karush-Kuhn-Tucker, Lagrange multipliers |
| reading weak | Oct. 11 - Oct. 15 | Thanksgiving | |
| Week 8 | Oct. 25 - Oct. 27 | Optimality and Duality | First and second order optimality, fundamental importance of duality |
| Week 9 | Nov. 1 - Nov. 3 | Algorithms for constrained mimization | Augmented Lagrangian, feasible directions |
| Week 10 | Nov. 8 - Nov. 10 | Interior-point methods | For both linear and nonlinear programs |
| Week 11 | Nov. 15 - Nov. 17 | General penalty, barrier methods | Convergence, implementation |
| Week 12 | Nov. 22 - Nov. 24 | Sequential quadratic programming methods | Applications, Maratos effect |
| Week 13 | Nov. 29 - Dec. 1 | First order methods | Alternating directions method of multipliers, general splitting methods, applications to hard discrete optimization problems |
Prof. Henry Wolkowicz, Department of Combinatorics and Optimization, University of Waterloo, 200 University Ave. W., Waterloo, ON N2L 3G1,
, by Henry Wolkowicz