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Heterogeneous network (HetNet) serves as one of the most promising technologies for the upcoming fifth-generation (5G) wireless networks. In this paper, we consider the joint design of the delay-aware user association and power control problem in an uplink HetNet. The problem of interest is to minimize the overall power consumption subject to the strict delay constraints, which is modeled as a non-convex and mixed-integer nonlinear programming (MINLP) problem. To solve this intractable problem, we first adopt the ℓ₁-norm approximation approach to convert the integer constraints into solvable forms. Then, an iterative algorithm is proposed to solve the reformulated problem based on the successive convex approximation (SCA). The proposed centralized SCA-based algorithm employs the arithmetic-geometric mean (AGM) approximation and it can be further improved by the reweighted ℓ₁ …