Timeline for Minimize smooth function $(x,y) \to f(x,y)$ subject to $x \perp y$
Current License: CC BY-SA 4.0
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| May 26, 2021 at 6:58 | comment | added | Dirk | "projected gradient descent non-convex" brings up several recent references. And with "Lagrange multipliers" I meant the standard approach to formulate optimality systems for constraint optimization problems. This is used to solve problems exactly. What you have in mind seems to be penalization approaches. | |
| May 25, 2021 at 19:06 | comment | added | dohmatob | @Dirk Thanks for the input. This is reassuring because The stuff I wrote above is pretty much projected gradient descent on the set $\{(x,y) \mid x \perp y = 0\}$. Do you have a ref for (even local) convergence of projected gradient descent ? Also, I'd rather not do lagrangian methods, because I want the constraint to be satisfied exactly. | |
| May 25, 2021 at 17:42 | comment | added | Dirk | I guess, projecting onto the set $\{(x,y)\mid x\bot y\}$ should be doable, so you could to projected gradient descent, if you want to. But how about solving the problem with by standard Lagrange multipliers? Depending on $f$, this might work directly. | |
| May 25, 2021 at 12:39 | history | asked | dohmatob | CC BY-SA 4.0 |