Class QuadraticConstraint

source code

           object --+        
                    |        
  properties.Function --+    
                        |    
properties.AtomicFunction --+
                            |
               object --+   |
                        |   |
      properties.Gradient --+
                            |
               object --+   |
                        |   |
       properties.Penalty --+
                            |
               object --+   |
                        |   |
    properties.Constraint --+
                            |
                           QuadraticConstraint

Known Subclasses:

• RGCCAConstraint

The proximal operator of the quadratic function

    f(x) = l * (x'Mx - c),

or

    f(x) = l * (x'M'Nx - c),

where M or M'N is a given symmatric positive-definite matrix. The
constrained version has the form

    x'Mx <= c,

or

    x'M'Nx <= c

if two matrices are given.

Parameters
----------
l : Non-negative float. The Lagrange multiplier, or regularisation
        constant, of the function.

c : Float. The limit of the constraint. The function is feasible if
        x'Mx <= c. The default value is c=0, i.e. the default is a
        regularisation formulation.

M : Numpy array. The given positive definite matrix. It is assumed that
        the first penalty_start columns must be excluded.

N : Numpy array. The second matrix if the factors of the positive-definite
        matrix are given. It is assumed that the first penalty_start
        columns must be excluded.

penalty_start : Non-negative integer. The number of columns, variables
        etc., to be exempt from penalisation. Equivalently, the first index
        to be penalised. Default is 0, all columns are included.