The iterative algorithm for minimum variance distortion- less response filter based on auxiliary-vector (IMVDR-AV) is generalized in this paper from different perspective. By extending the optimization criteria on filter design, it is generalized to an iterative algorithm of linear constrained minimum power filter (ILCMP-AV). Starting from this algorithm, we present an iterative algorithm of LCMP filter based on local optimization criterion (ILCMP-LOC) which converges rapidly by further generalizing the conditional optimization criterion on weighting coefficient computation. For any positive definite input auto- correlation matrix and any linear constraint, the ILCMP-AV algorithm recursively generates a sequence of auxiliary vectors by maximizing the magnitude cross correlation under some constraint conditions and its corresponding weighting coefficients by minimizing the filter output variance. Theoretical analysis illustrates that the combination of the updated filters and the weighted auxiliary vectors forms a sequence of filters that converges to the LCMP solution.