Paaßen, Benjamin ; Artelt, André ; Hammer, Barbara: Lecture Notes on Applied Optimization. 2019
Inhalt
- Contents
- Introduction
- Theory
- Basic Concepts of Optimization
- Optimization Problems and Formalization
- Standard Form
- Global and Local Optima
- Continuous versus Discrete Optimization Problems
- Differentiable Optimization
- Gradient, Hessian, and Taylor Expansion
- Searching for Optima with Gradient and Hessian
- Eigenvalue analysis
- Convex Optimization
- Duality
- Algorithms
- Analytical Methods
- Numeric Methods
- Unconstrained Optimization
- Gradient Descent
- Stochastic Gradient Descent / Adam
- Optimizing the Step Size
- Conjugate Gradient
- Newton's Method
- (L-)BFGS
- Trust Region Method
- Constrained Optimization
- Probabilistic Optimization
- Maximum Likelihood
- Maximum a posteriori
- Expectation Maximization
- Belief Propagation and Max-Product-Algorithm
- Convex Programming
- Heuristics
- Bibliography
- Acronyms
- Glossary
- Rules for Derivatives and Gradients