Optimization for Systems and Control
Table of Contents
- 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
Appendices
- Singular Value Decomposition
- Least Squares Problems
- Ordinary least squares
- Total least squares
- Robust least squares