We develop a source and mask co-optimization framework incorporating the minimization of edge placement error (EPE) and process variability band (PV Band) into the cost function to compensate simultaneously for the image distortion and the increasingly pronounced lithographic process conditions. Explicit differentiable functions of the EPE and the PV Band are presented, and adaptive gradient methods are applied to break symmetry to escape suboptimal local minima. Dependence on the initial mask conditions is also investigated. Simulation results demonstrate the efficacy of the proposed source and mask optimization approach in pattern fidelity improvement, process robustness enhancement, and almost unaffected performance with random initial masks.