Course: 2022/2023

Advanced Optimization and Decision Analytics

(19378)

The goal of this course is to become familiar with the main optimization modeling techniques and the solution algorithms that are being applied in Data Science. In this way, we provide the necessary tools and modern techniques of optimization for the efficient solution of many Data Science problems arising in diverse areas like Business, Health, Marketing, Finance and Engineering.
In particular, the objectives are:
1. Modeling and application of optimization methods for a series of general problems (linear models, discrete models, nonlinear models and also optimization under uncertainty)
2. Learn about the basic (mathematical) foundations that support the development of solution algorithms for the optimization problems mentioned above.
3. Study the main solution algorithms that are being applied to address problems in Data Science.
4. Use Python to apply tools of modern optimization techniques in an efficient way.

Skills and learning outcomes

Description of contents: programme

Contents:
1. Advanced Optimization Modeling
1.1. Algebraic modeling languages
1.2. Introduction to Pyomo
1.3. Examples
1.4. Automatic differentiation
2. Nonlinear Optimization
2.1. Introduction
2.2. Examples
2.3. Unconstrained Optimization
2.4. Constrained Optimization
2.5. Solution Algorithms
3. Optimization and Machine Learning
3.1. Introduction
3.2. Examples
3.3. Solution Algorithms
4. Optimization under uncertainty
4.1. Introduction
4.2. Simulation
4.3. Stochastic Programming
4.4. Examples

Learning activities and methodology

½ lectures with supporting materials available on the Web
½ practical sessions (computer labs with Python)

Assessment System

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

Basic Bibliography

- Bertsimas, Dimitris, and John Tsitsiklis . Introduction to Linear Optimization. Belmont, MA: Athena Scientific. 1997
- D Bertsimas, R Weismantel . Optimization over integers. Belmont: Dynamic Ideas. 2005
- Jorge Nocedal Stephen J. Wright. Numerical Optimization. Springer. 2006
- Sra, S., Nowozin, S., and Wright, S. J. Optimization for machine learning. Mit Press. 2012
- Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press. 2004

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