Modeling Piecewise Quadratic Objective Function
Published:
The generator offers are piecewise linear marginal cost function. Motivated by the electricity market example
Problem Description
Piecewise Linear Function
Piecewise Quadratic Function
General Convex Piecewise Function
Solutions
Solution 1: introducing binary variables
Solution 2: define black-box type objective functions
Solution 3: formulate epigraph with additional variables
A simple example
Example
\[f(x) = \begin{cases} x^2,& \text{if}\,0 \le x < 1 \\ 10 x^2 - 9,& \text{if}\, 1 \le x \end{cases}\]YALMIP code
More Thoughts
Limitations
Thanks Dr. Johan Löfberg for suggestions.