MA4311: Calculus of Variations - NPS Online
Overview
First and second order tests, Lagrange multipliers, Euler-Lagrange equation, non-smooth solutions, optimization with constraints, Weierstrass condition, optimal control of ODE systems, Pontryagin maximum principle. Applications may include: control and dynamical systems, estimation, weak formulations, Hamilton's variational principle, or others depending on the interests of the students.
Included in degrees & certificates
- 299
Prerequisites
- MA2121
Learning Outcomes
- Apply first and second order tests to solve unconstrained optimization problems.
- Apply Lagrange multipliers to solve optimization problems with equality constraints.
- Apply KKT conditions to solve general optimization problems with both equality and inequality constraints.
- Design deep neural networks using various types of activation functions and architectures.
- Use a deep learning package to train neural networks for regression problems.
- Apply techniques of the calculus of variations to derive the Euler-Lagrange equation.
- Minimize a cost functional with a fixed end.
- Solve problems with end-points not fixed.
- Optimize a cost functional with nonsmooth solutions.
- Solve isoperimetric problems and optimization with constraints.
- 2. Apply Pontryagin Maximum Principle to find optimal control for simple examples.
- 4. Find time optimal control for linear systems.
- Derive the Riccati equation for the Linear Quadratic Regulator problem (LQR).
- Solve LQR problems using the Riccati equation.
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