usage.txt

In this file, it is explained how to call AS-ZSL in Matlab to solve

                    min 0.5*||Ax-y||^2 + lambda*||x||_1
               s.t. sum(x) = 0

with given matrix A, vector y and non-negative scalar lambda.
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Usage.
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X = as_zsl(A,Y,LAMBDA)
X = as_zsl(A,Y,LAMBDA,OPTS)
[X,F] = as_zsl(...)
[X,F,AS_ZSL_INFO] = as_zsl(...)
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Input arguments.
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- A (required) is the matrix of covariates (each row is a sample),
- Y (required) is the response vector,
- LAMBDA (required) is the regularization parameter (or a vector of
                    regularization parameters sorted in descending order,
                    see below),
- OPTS (optional) is a structure with algorithm options (see below).
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Output arguments.
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- X is the vector of regression coefficients;
- F is the objective function value at X;
- AS_ZSL_INFO is a structure with the following fields:
  'it' is the number of iterations;
  'flag' is an integer describing the exit condition:
    0 if the optimality violation <= 'eps_opt'
      (default value of 'eps_opt' = 1e-3),
    1 if the number of iterations >= 'max_it'
      (default value of 'max_it' = 100000),
    2 if no sufficient decrease in the objective function has been obtained.
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Options.
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To change the values of the above parameters 'eps_opt'and 'max_it', use
the structure OPTS (it is one of the input arguments of 'as_zsl', see
above), having as field names the names of the parameters to be changed.
Anther parameter that can be changed in the same way is 'verbosity',
which can be set to true or false to have prints or not (the default value
of 'verbosity' is false).
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Using more regularization parameters.
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LAMBDA can even be a vector of regularization parameters sorted in
descending order. In this case, to solve a problem for each
regularization parameter, a warm start strategy is used and the output
values have columns, each one referring to the corresponding regularization
parameter.
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