- Introduction
- Mathematical framework
- Unimodality and convexity
- Optimization problems
- Optimality conditions
- Convergence and stopping criteria

- Linear Programming
- The linear programming problem
- The simplex method

- Quadratic Programming
- Quadratic programming algorithm
- System identification example

- Nonlinear Optimization without Constraints
- Newton and quasi-Newton methods
- Methods with direction determination and line search
- Nelder-Mead method

- Constraints in Nonlinear Optimization
- Equality constraints
- Inequality constraints

- Convex Optimization
- Convex functions
- Convex problems: Norm evaluation of affine functions
- Convex problems: Linear matrix inequalities
- Convex optimization techniques
- Controller design example

- Global Optimization
- Local and global minima
- Random search
- Multi-start local optimization
- Simulated annealing
- Genetic algorithms

- Optimization Methods: Summary
- Simplification of the objective function and/or the constraints
- Determination of the most efficient available algorithm
- Determination of the stopping criterion

- The MATLAB Optimization Toolbox
- Linear programming
- Quadratic programming
- Unconstrained nonlinear optimization
- Constrained nonlinear optimization

- Multi-Objective Optimization
- Problem statement
- Pareto optimality
- Solution methods for multi-objective optimization problems

- Integer Optimization
- Complexity
- Search
- Overview of integer optimization methods

- Multi-Criteria Controller Design: The LTI SISO Case
- Introduction
- The basic feedback loop
- General formulation of the basic feedback loop
- Internally stabilizing controllers

- Convex Controller Design Specifications
- Definition of affine and convex transfer function sets
- Engineering specification with respect to overshoot
- Engineering specification with respect to tracking a reference signal
- Engineering specifications in terms of norms of transfer functions
- Robust stability and plant uncertainty

- An Example of Multi-Criteria Controller Design
- The plant
- Engineering specifications
- General formulation of the basic feedback loop
- Linear Quadratic Gaussian design
- Example formulation of a robust controller design problem
- Computing the noise sensitivity and its gradient
- Computing the robustness constraint and its subgradient
- MATLAB implementation
- Discussion of the results

- Basic State Space Operations
- Cascade connection or series connection
- Parallel connection
- Change of variables
- State feedback
- Output injection
- Transpose
- Left (right) inversion

- Jury's Stability Criterion
- Singular Value Decomposition
- Least Squares Problems
- Ordinary least squares
- Total least squares
- Robust least squares