Numerical Methods for Optimization and Optimal Control

(3-0-0-3)

CMPE Degree: This course is Selected Elective for the CMPE degree.

EE Degree: This course is Selected Elective for the EE degree.

Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.

Technical Interest Groups / Course Categories: Threads / ECE Electives

Course Coordinator: Anthony Joseph Yezzi

Prerequisites: ECE 3084 [min D] or ECE 3550 [min D]

Catalog Description

Algorithms for numerical optimization and optimal control, Gradient-descent techniques, linear programming, numerical linear system solvers, second-order methods for optimizing performance of dynamical systems.

Textbook(s)

Course Outcomes

Write computer code to implement linear system constructs learned in prior S+C courses. 

Understand the types of errors than can arise in these implementations, and how to quantify them. 

Construct computer algorithms to solve other problems which don't benefit from closed form constructs acquired in previous 

Know which types of models should be paired with which types of numerical optimization algorithms based on properties such as convexi 

In cases were multiple choices of numerical optimization algorithms are suitable for a given problem, students will understand the relative advanta

Strategic Performance Indicators (SPIs)

N/A

Topic List

  1. Numerical Methods
    1. Review of numerical issues when using machine number systems
    2. Direct Linear systems solvers (LU, Cholesky, iterative refinement)
    3. Scalar nonlinear equation solvers (bisection, Newton, secant method)
    4. Numerical differentiation and Integration
  2. Optimization
    1. Introduction to nonlinear programming
    2. Optimality conditions for constrained and unconstrained problems
    3. Algorithms: gradient descent, Newton-Rhapson, conjugate-gradient techniques
    4. Least-square problems and algorithms
    5. Optimization problems with equality and inequality constraints
  3. Algorithms for optimal control problems
    1. Discrete-time optimal control: necessary optimality conditions
    2. Continuous-time optimal control: the Hamiltonian
    3. The linear-quadratic optimal control problem and feedback-based solution
    4. The Pontryagin's Maximum principle
    5. Examples: minimum-time problems and minimal-path problems