  In this paper, the problem of joint radio and computation resource management
over multi-channel is investigated for multi-user partial offloading mobile
edge computing (MEC) system. The target is to minimize the weighted sum of
energy consumption by jointly optimizing transmission time, local and edge
computation capacity allocation, bandwidth allocation and data partition. An
optimization problem is formulated, which is nonconvex and can not be solved
directly. Then, we transform the origin optimization problem into an equivalent
convex optimization problem. For general case of multi-user multi-channel, we
decouple the convex optimization problem into subproblems and an optimal
resource management strategy is obtained by adopting block coordinate descent
(BCD) method. To gain further insight, we investigate the optimal resource
management strategy for two special cases. First, consider the case of
multi-user shares single channel. Since the single-channel optimization problem
is reduced from the multi-channel optimization problem, the solution approach
of general case can be applied to this case, and the solving algorithm for this
case has low computation complexity, which is a combination of analytical and
bisection-search methods. Then, for the case of single-user occupies all
channel, the optimization problem is simplified and an optimal solving
algorithm with closed-form solutions is proposed.
