oppy Tutorials

Tutorials about how to use oppy.

Beginners Notebooks

• Solving the Rosenbrock Problem
  • Introduction
  • Minimization of the Rosenbrock function via oppy
    • Descent method using armijo and wolfe line search
    • Newtons method using armijo and wolfe line search
    • Compare different optimization methods using the wolfe line search
  • Conclusion: Comparison of convergence rates
• Solve the negative cosine problem
  • Introduction
  • Minimization Process
    • Armijo and wolfe linesearch with gradient descent method
    • Newton’s method using armijo and wolfe linesearch
    • Comparison of the different algorithms
  • Conclusion: Comparison of convergence rates
• Least-Squares Problems
  • Definition
  • Least-Squares Problems in Model Fitting
• Linear Least squares
  • Prediction of house sale prices
• Solving Nonlinear Least Squares Problems Using the Gauß-Newton Method
  • Introduction
  • Model Fitting via oppy
    • Preparation: Building the Sum of Squared Residuals (SSR)
    • Applying the Gauß-Netwon Method
      • a) Using the Gauß-Netwon Method with its Default Setting
      • b) Using the Gauß-Netwon Method with Further Options
    • c) Using the Levenberg-Marquardt Variant of the Gauß-Netwon Method
• Adjusting Parameters in a Nonlinear Model Using the Levenberg-Marquardt Method
  • 1. Introduction
  • 2. Example
    • Data:
    • Model:
    • Nonlinear Least-Squares Problem:
  • 3. Minimize the objective function \(f\)
  • 4. Graphical Illustration of the Solution
  • 5. Potential Issues
    • Poor Scaling - Example
    • Large Residuals - Example
• Solve a linear program
  • Notebook to demonstrate the Simplex Method
• How to solve an integer linear program
  • Notebook to demonstrate the Branch and Bound Method
• Solve a box constrained optimization problem
  • Notebook to demonstrate how to solve an optimization problem subject to box constraints via oppy

Advanced Notebooks

• Solving a Convex Multiobjective Optimization Problem
  • Solution with the Weighted-Sum Method (WSM)
  • Solution with Euclidian Reference Point Method (ERPM)
• Multiojective Optimization of the Fonseca Fleming function
  • Solution with the Pascoletti-Serafini method (PSM)
  • Solution with Euclidian Reference Point Method (ERPM)
  • Solution with Weighted-Sum Method (WSM)
• Using iterative methods to solve the Laplace equation
  • Theoretical introduction
  • Compute a first solution using the scipy sparse solver
  • Iterative Solvers
  • Krylov methods
  • Conclusion: Comparison of convergence rates
  • Krylov methods vs. scipy sparse solver
• Solve a linear-quadratic ODE Optimal Control Problem
  • Notebook to demonstrate how to solve an linear quadratic optimal control problem via oppy
• Solve a Lotka-Volterra based ODE Optimal Control Problem
  • Notebook to demonstrate how to solve a Lotka-Volterra optimal control via oppy