Numerical solutions of eigenvalue problems with linear constrains

As an example, one need to search the least or the least second eigenvalue and corresponded eigenvector of matrix A, under constraint Bx=c, where B is coefficient matrix, x is eigenvector under search, and c is a constant vector. How could I find some effective way to solve this type of problem efficiently.

Sounds like a quadratic program you could solve using JuMP maybe?

Looks like linear algebra - Linearly constrained eigenvalue problem - MathOverflow has an answer that might help, although you might have come across this already. This becomes much simpler if c=0.

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Thx for your help.
As Justin mentioned, this type of constrained eigenvalue problem cannot be reduced to generalized EV problem. I am not sure dealing with finding global minimum with constrains or solving linear equations would lead less computational cost.

IterativeSolvers lobpcg supports constraints of the form C x = 0. See the C matrix in LOBPCG · IterativeSolvers.jl.

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Sure, but this function does not support general linear constraint.

You can try formulating the problem as a semidefinite program with linear constraints then use JuMP.