  This work proposes a novel adaptive linearized alternating direction
multiplier method (LADMM) to convex optimization, which improves the
convergence rate of the LADMM-based algorithm by adjusting step-size
iteratively.The innovation of this method is to utilize the information of the
current iteration point to adaptively select the appropriate parameters, thus
expanding the selection of the subproblem step size and improving the
convergence rate of the algorithm while ensuring convergence.The advantage of
this method is that it can improve the convergence rate of the algorithm as
much as possible without compromising the convergence. This is very beneficial
for the solution of optimization problems because the traditional linearized
alternating direction multiplier method has a trade-off in the selection of the
regular term coefficients: larger coefficients ensure convergence but tend to
lead to small step sizes, while smaller coefficients allow for an increase in
the iterative step size but tend to lead to the algorithm's non-convergence.
This balance can be better handled by adaptively selecting the parameters, thus
improving the efficiency of the algorithm.
