Systems Optimization - Interactive curriculae of TU Ilmenau

PRELIMINARIES
1. Introduction, Motivation, and Preliminaries
- Importance of Systems Optimization
- Mathematical Preliminaries
- Convex sets and Convex Functions

PART - I : Steady-State Optimization Problems and Applications

Methods of Unconstrained Optimization Problems
2.1. First- and Second-Order Optimality Conditions
2.2. The Method of Steepest Descent
2.3. The Newton Method
2.4. The Levenberg-Marquardt Method
2.5. Quasi-Newton Methods
2.6. Line-search Methods
2.7. System of Nonlinear Equations
2.7a. Numerical Algorithms for Systems of Nonlinear Equations
2.7b. Numerical Solution Methods for Differential Algebraic Equations: backward differentiation formula (BDF), Single and Multiple-shooting, collocation methods

Methods of Constrained Optimization Problems
3.1. The Karush-Kuhn-Tucker Optimality Conditions
3.2. Convex Optimization Problems
3.3. Penalty Methods
3.4. Barrier and Interior-Point Methods
3.5. The Sequential Quadratic Programming (SQP) Method

Part-II: Dynamic Optimization Problems and Applications

4. Introduction to Dynamic Optimization
5. Direct Methods for Dynamic Optimization Problems
5.1. Collocation Methods for Dynamics Optimization Problems
5.2. Costate estimation
6. Introduction to Model-Predictive Control

Appendix
• A review on numerical linear algebra methods
• Introduction to 1D quadrature rules and orthogonal polynomial collocation
• A review on numerical methods of Ordinary Differential Equations (ODEs): numerical methods of initial value and boundary value ordinary differential equations - Euler method, Runge-Kutta, BDF, implicit Runge-Kutta,
• A brief introduction differential Algebraic Equations (DAEs) and Applications: The concept of Index in DAEs, Consistent Initialization, etc.
• A summary of the Classical Theory of Optimal Control Problems - the Pontryagin Principle - Indirect Methods