- Lecture September 27, 2018 - Introduction to the course, exams and grading, teaching material. Online Survey. A brief review on OR history. Paradigm for construction of mathematical models. An assignment problem. MATERIAL: Slide 1st lecture, Chap1-2 of Hillier, Lieberman - Introduction to Operations Research, McGraw-Hill Education (2015), Dantzig's memory,
- Lecture September 28, 2018 - A simple production planning problem MATERIAL: slide 2nd lecture, description of the production problem.
- Lecture October 4, 2018 - Basic defintion and classification of optimization problems A nonlilnear model of optimal sizing. MATERIAL: teaching notes Chapter 1; description of the optimal sizing problem;
- Lecture October 5, 2018 - Convex analysis: convex sets (definition and properties) and convex functions (definition). Convex optimization problem: definitions. A multiplant optimization problem. MATERIAL: teaching notes Chapter 2; Appendix B of D. Bertsekas, Nonlinear Programming- 2nd ed., description of the multiplant problem.
- Lecture October 11, 2018 - Convex optimization problem: theorem of equivalence of local and global minimizers. First and second order conditions for convexity of a function. (Ref. Appendix B of D. Bertsekas, Nonlinear Programming- 2nd ed., chapter 2 Teaching Notes)
- Lecture October 12, 2018 - Criteria for checking positive (semi)definiteness of a matrix. Convex and strictly convex quadratic functions: convexity criteria. Evaluation test in the class.
- Lecture October 18, 2018 - Concave optimization problem: defintion and non existence of interior solution. Quadratic functions. (Ref. chapter 2 Teaching Notes) -Descent and feasible directions.
- Lecture October 19, 2018 - First and second order characterization of descent directions. The case on unconstrained problem: first or necessary conditions.
- Lecture October 25, 2018 - Second order necessary conditionsfor unconstrained optimization. The convex uconstrained case. Exercise
- No Lecture October 26, 2018
- No Lecture November 1, 2018
- No Lecture November 2, 2018
- Lecture November 8, 2018 - 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)
- Lecture November 9, 2018 - Feasible direction of a polyhedron.
- Lecture November 15, 2018 - Optimization over a polyhedron: feasible directions, maximum stepsize for feasiblity, first order conditions.
- Lecture November 16, 2018 -
- Lecture November
- Lecture November
- Lecture November
- Lecture November
- Lecture December 6, 2018 - Definition of vertex of a polyhedron and theorem on the characterization (no proof) - Fundamental Theorem of LP (no proof)
- Lecture December 7, 2018 - Basic feasible solutions - Basic of the simplex method
- Lecture December 13, 2018 - Integer Linear Programming: basic concept. Integer polyhedron, total unimodularity (no characterization). - Upepr and lower bound - Solution of the continuous knapsack problem. The dual of the blending problem, the dual of the transportation problem.
- Lecture December 14, 2018
- Lecture December 15, 2018
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- 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.)
- Lecture November 5, 2017 - Optimization with inequality: Farkas' Lemma and the KKT conditions. (Ref. Chapt 5 of Teaching Notes).
- Lecture November 8, 2017 - The KKT conditions for inequality and equality constraints. The optimality condition for LP. (Ref. Chapt 6 of Teaching Notes)
- 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)).
- Lecture November 10, 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)).
- Lecture November 13, 2017 - Construction of priml-dual LP problems. Use of the KKT (duality) theorem to find pair of primal-dual solutions. Exercise from the exams.
- Lecture November 15, 2017 - Modelling absolute values in min function (min max).
- Lecture November 17, 2017 - Sensitivity analysis in LP
- Lecture November 20, 2017 - The dual of a blending problem.
- Lecture November 22, 2017 - Primal-dual relationships. The continuous knapsack example. Exercises.A blending model with advertising
- - Extreme point of convex sets. Vertex of a polyhedron: characterization theorem. Exercises. A simple lot sizing model. (Ref. material of the 15th lecture)
- - Fundamental theorem of Linear Programming (Ref. material of the 15th lecture)
- Lecture - 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.
- Lecture - Integer linear Programming: definition and first examples. The continuous knapsack problem: finding the otimal solution using duality. (Ref. material Chapter 10)
- Lecture Branch and Bound (Ref. material Chapter 10)
- Lecture - Branch and Bound: exercises (Ref. material Chapter 10)
- Lecture - Multiobjective optimization: Pareto optimality. An example. Exercise from a test exam