Al Holder - Professional Rose-Hulman Mathematics

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Math 348
Continuous Optimization

This course focuses on modeling and solving problems in continuous optimization, which includes the areas of mathematical programming, dynamic programming, and control theory. We will follow the text of P. Pedregal titled "Introduction to Optimization," which gives a wonderful introductory overview that highlights the commonality between the problem classes. Key topics include

  • linear and nonlinear programming: the necessity and sufficiency of the KKT conditions along with several algorithmic methods,
  • variational problems and dynamic programming: the Euler-Lagrange Equation and Bellman's equation,
  • optimal control: a brief introduction to Pontryagin's maximum principle.
Several examples will be used to motivate each problem class, and from this perspective the course is about developing the mathematical and algorithmic machinery to solve continuous optimization problems.