  In this paper an iterative minimization method is proposed to approximate the
minimizer to the double-well energy functional arising in the phase-field
theory. The method is based on a quadratic functional posed over a nonempty
closed convex set and is shown to be unconditionally energy stable. By the
minimization approach, we also derive an variant of the first-order scheme for
the Allen-Cahn equation, which has been constructed in the context of Invariant
Energy Quadratization, and prove its unconditional energy stability.
