Chip area, power consumption, execution time, off chip memory bandwidth, overall cache miss rate and Network on Chip (NoC) capacity are limiting the scalability of SoCs. Consider a workload comprising a sequential and multiple concurrent tasks and asymmetric or heterogeneous SoC architecture. A convex optimization framework is proposed, for selecting the optimal set of processing cores and allocating area and power resources among them, the NoC and the last level cache, under constrained total area, total average power, total execution time and off-chip bandwidth. The framework relies on analytical performance and power models of the processing cores, NoC and last level cache as a function of their allocated resources. Due to practical implementation of the cores, the optimal architecture under constraints may exclude several of the cores. Several asymmetric and heterogeneous configurations are explored. Convex optimization is shown to extend optimizations based on Lagrange multipliers. We find that our framework obtains the optimal chip resources allocation over a wide spectrum of parameters and constraints, and thus can automate complex architectural design, analysis and verification.