POGS ADMM-based graph form solver

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Setup

Once you have downloaded POGS, open MATLAB and type

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>> cd <pogs>/src/interface_matlab

in the MATLAB console. The string

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<pogs>

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>> pogs_setup

Alternatively typing

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>> pogs_setup gpu

will compile the GPU version.

MATLAB-specific usage

The MATLAB interface is a single MEX-function, with signature

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[x, y, l, optval] = pogs(A, f, g, params)

Inputs:

• 1

  A

  is the data matrix of dimension \(m n\).

• 1

  f

  and

  1

  g

  are structs with fields

  1

  h

  ,

  1

  a

  ,

  1

  b

  ,

  1

  c

  ,

  1

  d

  and

  1

  e

  , each of which must either be a vector of dimension \( m \) (resp. \( n \)) or a scalar. If a scalar is specified, then it is assumed that the scalar should be repeated \( m \) (resp. \( n \)) times. Multiple problems can be solved with the same matrix \( A \), if

  1

  f

  and

  1

  g

  are specified as struct arrays.

Optional Inputs:

• 1

  params

  is a struct with fields

  1

  rel_tol

  ,

  1

  abs_tol

  ,

  1

  rho

  ,

  1

  max_iter

  ,

  1

  quiet

  and

  1	adaptive_rho

  .

Outputs:

• 1

  x

  and

  1

  y

  are the solution vectors \(x^\star_\text{pogs}\) resp. \(y^\star_\text{pogs}\), and have dimension \( m \) resp. \( n \).

• 1

  l

  is the dual variable \(\lambda^\star_\text{pogs}\) corresponding to the constraint \(Ax = y\) and has dimension \( m \).

• 1

  optval

  is the value of the objective \(p^\star_\text{pogs}\) at the solution (\(p^\star_\text{pogs} = f(y^\star_\text{pogs}) + g(x^\star_\text{pogs})\)).

For more information type

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>> help pogs

\(h\)-Functions

The values

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f.h

1

g.h

1
2

kAbs,      kExp,     kHuber,   kIdentity, kIndBox01, kIndEq0,  kIndGe0,  kIndLe0,
kLogistic, kMaxNeg0, kMaxPos0, kNegEntr,  kNegLog,   kRecipr,  kSquare,  kZero

For example to specify that \(g_j(x_j) = |x_j|\) for \(j = 1\ldots 4\) and \(g_5(x_5) = I(x_5 = 0)\), use the syntax

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>> g.h = [kAbs(4); kIndEq0];

See Functions for a more detailed explanation of the functions and their usage.

Example Usage

See the examples listed on the left-hand side under Examples.