QC-MDPC (quasi cyclic moderate density parity check) code-based McEliece cryptosystems are considered to be one of the candidates for post-quantum cryptography. Decreasing DFR (decoding failure rate) is one of important factor for their security, since recent attacks to these cryptosystems effectively use DFR information. In this paper, we pursue the possibility of optimization-base decoding, concretely we examine ADMM (alternating direction method of multipliers) based method, a recent developing method in optimization theory. Further, RSPA (reproducing sum-product algorithm), which efficiently reuse outputs of SPA (sum-product algorithm) is proposed for further reduction of DFR. By numerical simulations, we show that the proposing scheme shows considerable decrement in DFR compared to the conventional decoding methods such as BF (bit-flipping algorithm) or SPA.