Course: 2024/2025

Optimization Techniques

(13707)

Requirements (Subjects that are assumed to be known)

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

1. Formulating optimization models for decision-making in diverse application areas.
2. Analyzing and solving optimization problems of dynamic 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.
1. Capacity for analysis and synthesis.
2. Problem solving and mathematical modeling.
3. Oral and written communication.

Skills and learning outcomes

Description of contents: programme

-Topic 1. Deterministic dynamic optimization.
1.1. Motivation, formulations and examples.
1.2. Computation of optimal policies; optimality equations; recursive solution; computer-based solution.
1.3. Applications and examples.
-Topic 2. Unconstrained nonlinear optimization (ONL).
2.1. Motivation and examples; local and global optima; convexity; optimality conditions; algebraic solution.
2.2. Algebraic solution; computer-based solution.
2.3. Applications and examples.
-Topic 3. Equality-constrained NLO.
3.1. Motivation and examples; Lagrange multipliers; optimality conditions.
3.2. Algebraic solution; computer-based solution.
3.3. Applications and examples.
-Topic 4. Inequality-constrained NLO.
4.1. Motivation and examples; Karush-Kuhn-Tucker multipliers; optimality conditions.
4.2. Algebraic solution; computer-based solution.
4.3. Applications and examples.
-Topic 5. Numerical solution of unconstrained NLO problems.
5.1. Newton's method; computer implementation.
5.2. Speed of convergence; possible divergence; sensitive dependence.

Learning activities and methodology

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.

Assessment System

- % end-of-term-examination 0
- % of continuous assessment (assigments, laboratory, practicals...) 100

Calendar of Continuous assessment

Extraordinary call: regulations

Basic Bibliography

- F.S. Hillier and G.J. Lieberman. Introduction to Operations Research. McGraw-Hill. 2010
- H.A. Taha . Operations Research: An Introduction . Prentice Hall. 2011

Additional Bibliography

- K. Lange. Optimization. Springer. 2004

The course syllabus may change due academic events or other reasons.