MATLAB scripts for alternating direction method of multipliers
2014-11-27 16:33
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MATLAB scripts for alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. EcksteinThis page gives MATLAB implementations of the examples in our
paper on distributed optimization with the alternating direction method of multipliers.
These scripts are serial implementations of ADMM for various problems. In cases where the scripts solve distributed consensus problems (e.g., distributed
-regularized
logistic regression), the code runs serially instead of in parallel. These scripts give an idea of the structure and flavor of ADMM; an implementation in C/C++ that follows the structure laid out in our scripts and exploits parallelism can be competitive with
state-of-the-art solvers for these problems. These are presented in MATLAB for readability. Unless otherwise noted on this page, most scripts stand alone and work in Matlab without further modification. Some scripts may require CVX.
As output, each example script displays the primal residual
, the primal feasibility
tolerance
, the dual residual
,
and the dual feasibility tolerance
. See section 3.3 of the paper
for more details on these quantities. Also included are plots of the objective value and the primal and dual residual by iteration. Note that the objective value at any particular iteration can go below the true solution value
because
the iterates need not be feasible (e.g., if the constraint is
, we can have
for
some
).
You can use the grabcode function
built in to MATLAB to obtain these codes. Please report any issues to the authors.
Examples
Basis pursuitADMM function
Example
Sparse inverse covariance selection
ADMM function
Example
Huber fitting
ADMM function
Example
Intersection of polyhedra
ADMM function
Example
Lasso
ADMM function
Example
Lasso with LSQR, an iterative method for solving sparse systems
ADMM function
Example
Least absolute deviations
ADMM function
Example
Linear programming
ADMM function
Example
-regularized logistic regression
ADMM function
Example
Distributed
-regularized logistic regression
ADMM function - also requires l2_log, l2_log_grad, record_bfgs_iters,
and LBFGS-B for Matlab.
Example
Regressor selection (nonconvex problem)
ADMM function
Example
Quadratic programming
ADMM function
Example
Sum-of-norms regularization (group lasso)
ADMM function
Example
Sum-of-norms regularization (group lasso) with feature splitting
ADMM function
Example
Support vector machine
ADMM function
Example
Total variation minimization
ADMM function
Example
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