We consider a general multi-user mobile cloud computing system where each mobile user has multiple independent tasks. These mobile users share the communication resource while offloading tasks to the cloud. We aim to jointly optimize the offloading decisions of all users as well as the allocation of communication resource, to minimize the overall cost of energy, computation, and delay for all users. The optimization problem is formulated as a non-convex quadratically constrained quadratic program, which is NP-hard in general. An efficient approximate solution is proposed by using separable semidefinite relaxation, followed by recovery of the binary offloading decision and optimal allocation of the communication resource. For performance benchmark, we further propose a numerical lower bound of the minimum system cost. By comparison with this lower bound, our simulation results show that the proposed algorithm gives nearly optimal performance under various parameter settings.
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