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Ultrasound elastography has been widely applied in clinical diagnosis. To produce high-quality elastograms, displacement estimation is important to generate fine displacement map from the original ratio-frequency signals. Traditional displacement estimation methods are based on the local information of signals pair, such as cross-correlation method, phase zero estimation. However, the tissue movement is nonlocal during realistic elasticity process due to the compression coming from the surface. Recently, regularized cost functions have been broadly used in ultrasound elastography. In this paper, we tested the using of analytic minimization of adaptive regularized cost function, a combination of different regularized cost functions, to correct the displacement estimation calculated by cross-correlation method directly or by lateral displacement guidance. We have demonstrated that the proposed method exhibit obvious advantages in terms of imaging quality with higher levels of elastographic signal-to-noise ratio and elastographic contrast-to-noise ratio in the simulation and phantom experiments respectively.