© 2018 IEEE. LIC (Local Intensity Compensation) is an intra-frame motion compensation for video coding, and was a candidate for HEVC. To obtain reference blocks and their coefficients in linear combination, Inoue et al. have applied AHIT (Accelerated Hard Iterative Thresholding) as a solver. However, this algorithm is heuristic; then, this paper proposes to use a sophisticated convex optimization solver ADMM (Alternating Direction Method of Multipliers). Experimental results demonstrate that our method provides higher PSNR values in the same reference block numbers than the conventional method.