A graph-based decomposition method for convex quadratic optimization with indicators

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining term in objective is sparse. We use a graphical representation of support Q, and show that if graph path, then can solve associated problem polynomial time. This enables us to construct compact extended formulation for closure hull epigraph mixed-integer problem. Furthermore, motivated by inference models, propose novel decomposition method class general (sparse) strictly diagonally dominant which leverages efficient algorithm path case. Our computational experiments demonstrate effectiveness proposed compared state-of-the-art solvers.