Lectures

  1. Lecture September 25, 2017 - Introduction to the course, exams and grading, teaching material. A brief review on OR history. Paradigm for  construction of mathematical models.  An assignment problem. (Ref. material of the 1st lecture)
  2. Lecture September 27, 2017 - An investment optimization model.  A production planning problem (Ref. material of the 2nd lecture)
  3. Lecture October 2, 2017 - Basic defintion and classification of optimization problems A nonlilnear model of optimal sizing.
  4. Lecture October 4, 2017 - Convex analysis: convex sets (definition and properties) and convex functions (definition). Convex optimization problem: definition (Ref. Appendix B of D. Bertsekas, Nonlinear Programming- 2nd ed.). A multiplant optimization problem and graphical solution.
  5. Lecture October 6, 2017 - Convex optimization problem: definition and theorem of equivalence of local  and global minimizers (Ref. Appendix B of D. Bertsekas, Nonlinear Programming- 2nd ed., chapter 2 Teaching Notes)
  6. Lecture October 9, 2017 - Concave optimization problem: defintion and non existence of interior solution. Quadratic functions. Convex and strictly convex quadratic functions: convexity criteria.  (Ref. chapter 2 Teaching Notes)
  7. Lecture October 11, 2017 -  Criteria for checking positive (semi)definiteness of a matrix. Quadratic functions. Exercise from exam tests of June 27, 2016 and July 19, 2017, June 15, 2017. (Ref material of the 4th lecture)
  8. Lecture October 13, 2017 -  Descent and feasible directions.
  9. Lecture October 16, 2017 -  First and second order characterization of descent directions. The case on unconstrained problem: first order necessary conditions.
  10. Lecture October 18, 2017 - Second order necessary conditionsfor unconstrained optimization. The convex uconstrained case.
  11. Lecture October 20, 2017 -The gradient method. A production model from the text exam. (Ref. Chapter 3 (pp236-238, 257-259) of D. Bertsekas, Nonlinear Programming- 3rd ed. - material of the lecture)
  12. Lecture October 23, 2017 - Feasible direction of a polyhedron. Exercise from text exams.
  13. Lecture October 25, 2016 - Optimization over a polyhedron: feasible directions, maximum stepsize for feasiblity, first order conditions.
  14. Lecture October 30, 2017 -  Optimization with linear equality: the Lagrangian conditions.  (ref. Chapt 5 of Teaching Notes or Example 4.1.2 of Chapter 4 of D. Bertsekas, Nonlinear Programming- 3rd ed.)  
  15. Lecture November 6, 2017 - Optimization with inequality: Farkas' Lemma and the KKT conditions.  (Ref. Chapt 5 of Teaching Notes).
  16. Lecture November 8, 2017 - The KKT conditions for inequality and equality constraints. The optimality condition for LP. (Ref. Chapt 6 of Teaching Notes)
  17. Lecture November 10, 2017 - Duality for LP: weak  duality theorem (Ref. Chapt 7 of Teaching Notes and Chapt 4 Kwon, Roy H. Introduction to linear optimization and extensions with MATLAB, CRC Press (2014)).
  18. Lecture November 13, 2017 - Duality for LP: strong duality theorem (Ref. Chapt 7 of Teaching Notes and Chapt 4 Kwon, Roy H. Introduction to linear optimization and extensions with MATLAB, CRC Press (2014)). 
  19. Lecture November 15, 2017 - Construction of priml-dual LP problems. Use of the KKT (duality) theorem to find pair of primal-dual solutions. Exercise from the exams.
  20. Lecture November 17, 2017 -  Modelling absolute values in min function (min max).
  21. Lecture November 20, 2017 - Sensitivity analysis in LP
  22. Lecture November 22, 2017 - The dual of a blending problem.
  23. Lecture November 24, 2017 - Primal-dual relationships. The continuous knapsack example. Exercises.A blending model with advertising
  24. Lecture November 27, 2017 - Extreme point of convex sets. Vertex of a polyhedron: characterization theorem. Exercises. A simple lot sizing model. (Ref. material of the 15th lecture)
  25. Lecture November 29, 2017 - Fundamental theorem of Linear Programming (Ref. material of the 15th lecture)
  26. Lecture December 1, 2017 - The standard form of LP. Basic feasible solutions and vertex. The reduced problem and the reduced cots. A blending model with advertsing and logical constraints.
  27. Lecture December 11, 2017 - Integer linear Programming: definition and first examples. The continuous knapsack problem: finding the otimal solution using duality. (Ref. material Chapter 10)
  28. Lecture December 13, 2017 - Branch and Bound (Ref. material Chapter 10)
  29. Lecture December 15, 2017 - Branch and Bound: exercises (Ref. material Chapter 10)
  30. Lecture December 18, 2017 - Multiobjective optimization: Pareto optimality. An example. Exercise from a test exam