This course focuses on the basic methods for solving linear and
nonlinear constrained optimization problems, including the direct
discretization of optimal control problems, making special emphasis in the
educated use of the state-of-the-art routines offered by Matlab’s optimization toolbox.
Most of the examples and exercises presented in this course are derived from actual
applications in the fields of mechanics and robotics.
The core of the course is organized into 3 parts, each part focusing on the understanding of one family of optimization problems. In each part, at least one practical problem will be discussed in detail and subsequently solved using Matlab:
1.
Linear optimization problems. Simplex method.
2.
Unconstrained nonlinear problems. Necessary and sufficient conditions for a minimum. Basic descent
methods, Newton methods.
3.
Constrained nonlinear problems. Necessary and sufficient conditions for a minimum. Penalty and
barrier methods, Lagrange methods, Sequential quadratic programming methods.
Following this core content, an overview of the related fields of Neural Networks, Calculus of Variations, and Optimal Control are offered.
Each part of the course comprises plenary lectures, exercises on the blackboard, as well as computer exercises using Matlab. Most of the software presented in the course is written live during the lectures and exercises. During the computer exercises, the students are trained to tackle practical problems using Matlab.
Learning objectives:
The goal of the course is to train the students to tackle practical optimization problems efficiently using tools like Matlab.
Literature:
Luenberger, D. G. (1984). Linear and nonlinear programming. Columbus,
Ohio: Addison-Wesley.
Martins, J. R., & Ning, A. (2021). Engineering design optimization.
Cambridge University Press.
Gill, P. E., Murray, W., & Wright, M. H. (2019). Practical
optimization. Society for Industrial and Applied Mathematics.
Fletcher, R. (2013). Practical methods of optimization. John Wiley &
Sons.
This is an advanced textbook by the famous developers of quasi-Newton
methods.
Boyd, S., Boyd, S. P., & Vandenberghe, L. (2004). Convex
optimization. Cambridge university press.
Brunton, S. L., & Kutz, J. N. (2022). Data-driven science and engineering: Machine
learning, dynamical systems, and control. Cambridge University Press. |
