Optimization with equation constraint

[LY]

Hi!

I'm using Manopt to deal with a problem like this:

I'm wondering whether I can transfer this problem to another problem， and are there any special requirements on the regulation parameter \lambda?

Sincerely,

YL

[Nicolas Boumal]

Hello,

The question of how to deal with constraints on manifolds ($g(U) = 0$) comes up from time to time: you can find some pointers in posts on this forum (use the search bar at the top).

For example, the post here may help:

https://groups.google.com/g/manopttoolbox/c/3S_k4ZPt7Rg/m/9rpXO2EoAwAJ

As you will see, there is no "definite" answer to this. But there are reasonable things to try.

Best,

Nicolas