2025 SDG 4th biweekly report

Review of the past two weeks

During the last two weeks, the optimization package in BoundaryValueDiffEq.jl has been changed to OptimizationIpopt.jl, and some of the issue with this package is now resolved: Relax Matrix type in IpoptCache, Use OptimizationIpopt.

After some conversation with Chris, the basic idea is clear and some of the previous confusion are resolved, for example, the constraints should be above the boundary conditions, use the sparse detector in the constraints partto get the banded Jacobian of hte constraints, etc. In the past two weeks, I have spent most of the time for finding the issue with the current implementation of optimal control interface, but it seems the solving process is still not working, my intial guess is the misappropriate usage of control variable in the collocation part, I will try to locate hte exact issue.

TODOs in next two weeks

In the following two weeks, there are a few TODOs:

1. Finalize the interface for optimal control problems, make the solving process converging.
2. Finalize a suitable convention for the cost function in formulating optimal control problems, mainly about the interpolating and integral of control variables.