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This paper studies a joint optimization problem of sub-carrier assignment and power allocation in Orthogonal Frequency Division Multiple Access (OFDMA) wireless networks. A major challenge in solving the optimization problem is non-convexity caused by the combinatorial nature of sub-carrier assignment problem and/or non-convex objective functions. To address the combinatorial complexity, the authors formulate the resource allocation problem as an optimization problem with continuous variables. They propose a novel approach based on a Penalty function Method and an Interior Point Method (PM/IPM) to solve the problem. In specific, using a two-step implementation, the penalty method is applied first to convert the non-convex feasible region to a convex one.
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