Students are expected to have completed courses with contents in linear algebra, multivariable differential calculus, statistics, business administration and computer programming.

CORE COMPETENCES: 1. Formulating optimization models for decision-making in diverse application areas. 2. Analyzing and solving optimization problems of linear, integer and nonlinear types, through the formulation and solution of their optimality conditions. 3. Using software tools for formulating and solving optimization models. 4. Interpreting the numerical solutions of optimization models in decision-making terms. TRANSVERSAL COMPETENCES: 1. Capacity for analysis and synthesis. 2. Problem solving and mathematical modeling. 3. Oral and written communication.

Topic 1.1. Linear optimization (LO). Operations research; LO models; formulations and applications; computer-based solution. Topic 1.2. Graphical solution; sensitivity analysis. Topic 1.3. The fundamental theorem of LO; basic feasible solutions and vertices; the simplex method. Topic 1.4. Duality in LO. Topic 1.5. Optimal network flow models. Topic 2.1. Integer optimization models; linear relaxations; optimality gap; graphical and computer solution. Topic 2.2. The Branch and Bound method. Topic 2.3. Combinatorial optimization models; strengthening formulations; valid inequalities. Topic 3.1: Unconstrained non-linear optimization (NLO). Motivation and examples; local and global optima; convexity; optimality conditions; numerical solution. Topic 3.2. Equality-constrained NLO. Motivation and examples; Lagrange multipliers; optimality conditions; numerical solution. Topic 3.3. Inequality-constrained NLO. Motivation and examples; Karush-Kuhn-Tucker multipliers; optimality conditions; numerical solution.

Theory (3 ECTS). Theory classes with supporting material in Aula Global. Practice (3 ECTS). Model formulation and problem-solving classes. Computing classes. The teaching methodology will have a practical approach, being based on the formulation and solution of problems drawn from diverse application areas, both in the practical classes and in the theory classes, as motivation and illustration of the theory. There will be a weekly individual tutoring session.