Skip to content

Commit

Permalink
Update README.md
Browse files Browse the repository at this point in the history
  • Loading branch information
pronenewbits authored May 3, 2020
1 parent 2113690 commit 54f7711
Showing 1 changed file with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion README.md
Original file line number Diff line number Diff line change
Expand Up @@ -89,7 +89,7 @@ b) More optimal than the previous iteration.
Using that fact, we can easily add another termination condition <img src="documentation_resources/eq_render/k_max_iter.gif" align="bottom"/> beside KKT condition <img src="documentation_resources/eq_render/term_clause.gif" align="top"/> to make sure the MPC calculation still satisfy the real-time requirement. The other option is to use a real-time timer as the termination condition. We then can use the not-the-most-optimal-but-still-feasible solution as the controller output.

#### Active Set: Wrap it up
The Active Set pseudo code then can be described as:
The Active Set pseudo code then can be redescribed as:
<p align="center"><img src="documentation_resources/ActiveSet_final.png" title="Hopefully this will be easier to understand than before?"/></p>

For more explanation about ASM, [these slides](https://people.cs.umu.se/eddiew/optpde2016/QP.pdf) or these pages ([here](https://neos-guide.org/content/quadratic-programming) and [here](https://neos-guide.org/content/quadratic-programming-algorithms)) are quite good at explaining the mechanism behind active set for quadratic programming problem. But for more in-depth treatment of this algorithm, the best resource is of course [Nocedal & Wright's Numerical Optimization](https://www.google.com/books/edition/Numerical_Optimization/7wDpBwAAQBAJ?hl=en&gbpv=0), chapter 16. Just be aware, the tutorials I linked (and many QP formulation) use inequality constraint in the form <img src="documentation_resources/eq_render/ax_geq_b.gif" align="bottom"/> while we use <img src="documentation_resources/eq_render/ax_leq_b.gif" align="bottom"/> (just multiply the inequality with <img src="documentation_resources/eq_render/-1.gif" align="bottom"/> to change from one form to another).
Expand Down

0 comments on commit 54f7711

Please sign in to comment.