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In this paper, we formulate the utility functions of distortion and peak signal-to-noise ratio (PSNR) which are generally used for the performance evaluation of video coding applications as the utility functions. The convexity property of these utility functions is analyzed in the original domain and transformed domain of an optimization variable. From this analysis, we derive joint optimization scheme with congestion control through the utility matching between TCP layer and video coding layer. Experimental results show that the overall PSNR increases and the variation of quality among the utility functions is reduced.