Class SOCPSectorNeutrality

  • All Implemented Interfaces:
    Function<Vector,​Double>, RealScalarFunction

    public class SOCPSectorNeutrality
    extends SOCPPortfolioConstraint
    Transforms a sector neutral constraint into the compact SOCP form.

    The sector neutral constraint is: \[ \sum_{j\in S_i}(w_j^0+x_j)=0,\quad i=1,\ldots,k, \] where \(S_i\) is the \(i\)th section indicator. By letting \(y=x+w^{0}\), the sector neutral constraint can be written as: \[ \sum_{j\in S_i}y_{j}=0, i=1,\cdots,k. \] And it is equivalent to: \[ ||(\sum_{j\in S_{i}}e_{j})^{\top}y||_{2}\leq 0. \] As a result the standard SOCP form of the sector neutral constraint can be written as: \[ ||(\sum_{j\in S_{i}}e_{j})^{\top}y||_{2}\leq 0\Longleftrightarrow ||A_{i}^{\top}z+C_{i}||_{2}\leq b^{\top}_{i}z+d_{i},\quad i=1,\cdots,k\\ A_{i}^{\top}=\sum_{j\in S_{i}}e^{\top}_{j},\; C_{i}=0,\; b_{i}=0_{n\times 1},\; d_{i}=0,\; z=y. \]
    See Also:
    "Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."
    • Constructor Detail

      • SOCPSectorNeutrality

        public SOCPSectorNeutrality​(Vector w_0,
                                    Vector[] S,
                                    double epsilon)
        Constructs a sector neutral constraint.
        Parameters:
        w_0 - the initial position
        S - the sector indicators
        epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
      • SOCPSectorNeutrality

        public SOCPSectorNeutrality​(Vector w_0,
                                    Vector[] S)
        Constructs a sector neutral constraint.
        Parameters:
        w_0 - the initial position
        S - the sector indicators
    • Method Detail

      • bias

        public double bias​(Vector y)
        Computes the amount of deviation from neutrality, hence bias.
        Parameters:
        y - the positions
        Returns:
        the sector bias
      • evaluate

        public Double evaluate​(Vector y)
        Description copied from interface: Function
        Evaluate the function f at x, where x is from the domain.
        Parameters:
        y - x
        Returns:
        f(x)
      • dimensionOfDomain

        public int dimensionOfDomain()
        Description copied from interface: Function
        Get the number of variables the function has. For example, for a univariate function, the domain dimension is 1; for a bivariate function, the domain dimension is 2.
        Returns:
        the number of variables
      • dimensionOfRange

        public int dimensionOfRange()
        Description copied from interface: Function
        Get the dimension of the range space of the function. For example, for a Rn->Rm function, the dimension of the range is m.
        Returns:
        the dimension of the range