I have a research problem that I have reduced to the following problem which seems to be hard:
Find $\mathbf{x}\in \mathbb{B}^N$ $(\mbox{where }\mathbb{B}= \{0,1\})$ which is $K$-sparse and which satisfies the following $$|e_{\pi(1)}^Tx|\ge|e_{\pi(2)}^Tx|\ge\cdots\ge|e^T_{\pi(N)}x|$$ where $U=[e_1\cdots e_N]$ is a unitary matrix and $\pi(1),\cdots,\ \pi(N)$ gives the indices of the decreasingly ordered eigenvalues of the matrix $B=U\Lambda U^T$ where $B$ is positive definite.
I have some information about the $B$ matrix, like it is positive definite and tridiagonal and it is diagonally dominant.
I want to know if there are some properties that $supp(x)$ has to satisfy. This is all I need actually.