  We propose a simple iterative (SI) algorithm for the maxcut problem through
fully using an equivalent continuous formulation. It does not need rounding at
all and has advantages that all subproblems have explicit analytic solutions,
the cut values are monotonically updated and the iteration points converge to a
local optima in finite steps via an appropriate subgradient selection.
Numerical experiments on G-set demonstrate the performance. In particular, the
ratios between the best cut values achieved by SI and those by some advanced
combinatorial algorithms in [Ann. Oper. Res. 248 (2017) 365] are at least
$0.986$ and can be further improved to at least $0.997$ by a preliminary
attempt to break out of local optima.
