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Mathematical Optimization for Engineers

Learn the mathematical and computational basics for applying optimization successfully. Master the different formulations and the important concepts behind their solution methods. Learn to implement and solve optimization problems in Python through the practical exercises.

Hay una sesión disponible:

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Comenzó el 4 oct
Termina el 22 dic
8 semanas estimadas
6–8 horas por semana
Al ritmo del instructor
Con un cronograma específico
Verificación opcional disponible

Sobre este curso

Omitir Sobre este curso

Today, for almost every product on the market and almost every service offered, some form of optimization has played a role in their design.

However, optimization is not a button-press technology. To apply it successfully, one needs expertise in formulating the problem, selecting and tuning the solution algorithm and finally, checking the results. We have designed this course to make you such an expert.

This course is useful to students of all engineering fields. The mathematical and computational concepts that you will learn here have application in machine learning, operations research, signal and image processing, control, robotics and design to name a few.

We will start with the standard unconstrained problems, linear problems and general nonlinear constrained problems. We will then move to more specialized topics including mixed-integer problems; global optimization for non-convex problems; optimal control problems; machine learning for optimization and optimization under uncertainty. Students will learn to implement and solve optimization problems in Python through the practical exercises.

De un vistazo

  • Institución: RWTHx
  • Tema: Ingeniería
  • Nivel: Intermediate
  • Prerrequisitos:

    You should have basic knowledge of linear algebra, vector calculus and ordinary differential equations. Familiarity with numerical computing is helpful but not required; programming tasks will be kept basic and simple. You will write simple Python scripts in Jupyter notebooks. We will provide some basic Python tutorials.

  • Idioma: English
  • Transcripción de video: English

Lo que aprenderás

Omitir Lo que aprenderás
  • Mathematical definitions of objective function, degrees of freedom, constraints and optimal solution
  • Mathematical as well as intuitive understanding of optimality conditions
  • Different optimization formulations (unconstrained v/s constrained; linear v/s nonlinear; mixed-integer v/s continuous; time-continuous or dynamic; optimization under uncertainty)
  • Fundamentals of the solution methods for each these formulations
  • Optimization with machine learning embedded
  • Hands-on training in implementing and solving optimization problems in Python, as exercises

Plan de estudios

Omitir Plan de estudios

Week 1: Introduction and math review

  • Mathematical definitions of objective function, degrees of freedom, constraints and optimal solution with real-world examples
  • Review of some mathematical basics needed to take us through the course

Week 2: Unconstrained optimization

  • Basics of iterative descent: step direction and step length
  • Common algorithms like steepest descent, Newton’s method and its variants and trust-region methods.

Week 3: Linear optimization

  • KKT conditions of optimality for constrained problems
  • Simplex method
  • Interior point methods

Week 4: Nonlinear optimization

  • Penalty, log-barrier and SQP methods

Mixed-integer optimization

  • Branch and bound method for mixed-integer linear problems

Week 5: Global optimization

  • Branch and bound method for nonlinear non-convex problems
  • Constructing relaxations
  • Different formulations and their numerical performance
  • Stochastic methods, genetic algorithm and derivative free methods

Week 6: Dynamic optimization

  • Full discretization, single-shooting and multi-shooting methods
  • Nonlinear model predictive control

Week 7: Machine learning for optimization

  • Mechanistic, data-driven and hybrid modelling
  • Basics of training machine learning models
  • Optimization with machine learning embedded

Week 8: Optimization under uncertainty

  • Parametric optimization
  • Two stage stochastic problems
  • Robust optimization via semi-infinite problems

Acerca de los instructores

¿Quién puede hacer este curso?

Lamentablemente, las personas residentes en uno o más de los siguientes países o regiones no podrán registrarse para este curso: Irán, Cuba y la región de Crimea en Ucrania. Si bien edX consiguió licencias de la Oficina de Control de Activos Extranjeros de los EE. UU. (U.S. Office of Foreign Assets Control, OFAC) para ofrecer nuestros cursos a personas en estos países y regiones, las licencias que hemos recibido no son lo suficientemente amplias como para permitirnos dictar este curso en todas las ubicaciones. edX lamenta profundamente que las sanciones estadounidenses impidan que ofrezcamos todos nuestros cursos a cualquier persona, sin importar dónde viva.

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