Sequential SOS

[JOlucak]

A first implementation of sequential SOS is available. It works fine and we obtain the same results as in bisos.

This thread is meant to keep track of certain known issues.

[JOlucak]

• Different results for GTM 4D example (results (level set) is worse, linesearch does not work. Check where the difference come from.
• Improve building-time i.e. more efficient implementation
• Check why mosek throws an error during the linesearch
• Clean up constructor and move code to buildproblem
• Look and implement on more sophisticated line-search algorithms

[tcunis]

[ ] Handle Gram decision variables

[JOlucak]

• Adapt line search algorithm (probably low level solver)

[JOlucak]

Current status

• The linesearch-solver using Mosek is replaced by a simple bisection
• A verbosity option is added showing the iteration, current cost, difference in primal and dual variables
• Implemented some examples

[JOlucak]

Some new issues occured that need to be clarified

• Cost is non decresing

• Some constraint are not fulfilled in the reachability problem. The storage function zero level set at t = T i.e. V(T,x) \leq 0 is outside the pre-defined terminal set

[JOlucak]

Current Status and To-Dos 06.05.2024

• Sequential approach from original paper works
• Extended to quadratic cost and Hessian estimation using BFGS
• First version of filter linesearch implemented (naive implementation)

To Dos:

• Clean up examples (linear and quadratic)
• Rename examples
• Clean up build problem
• Improve globalization to more sophisticated methods