Class SOCPNoTradingList2

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

    public class SOCPNoTradingList2
    extends SOCPPortfolioConstraint
    Transforms a black list (not to trade a new position) constraint into the compact SOCP form.

    The black list constraint is: \[ x_{j}=0, \] for j in the black list. By letting \(y=x+w^{0}\),\(\bar{y}=|x+w^{0}|\) and \(\bar{x}=|x|\), the black list constraints are changed to: \[ y_{j}=w^{0}_{j},\;\bar{y}_{j}=|w^{0}_{j}|,\;\bar{x}_{j}=0, \] for j in the black list. Denote the black list index set as \(BL\), i.e. \(BL=\{j|x_{j}=0\}\). As \(y_{j}=x_{j}+w_{j}^{0}\), the set \(BL\) can be written as \(BL=\{j|y_{j}=w_{j}^{0}\}\). The black list constraints can be written in the following form: \[ ||D_{BL}(y-w^{0})||_{2}\leq0,\;||D_{BL}(\bar{y}-|w^{0}|)||_{2}\leq0,\;||D_{BL}\bar{x}||_{2}\leq0, \] where \(D_{BL}\) is a diagonal matrix. The \(k\)th diagonal entry of \(D_{BL}\), \(D_{BL}(k,k)\), is \(1\) if \(k\in BL\), otherwise it is \(0\). These constraints can be transformed into the standard SOCP form: \[ ||D_{BL}(y-w^{0})||_{2}\leq0\Longleftrightarrow ||A_{1}^{\top}z+C_{1}||_{2}\leq b^{\top}_{1}z+d_{1}\\ A_{1}^{\top}=D_{BL},\; C_{1}=-D_{BL}\times w^{0},\; b_{1}=0_{n\times 1},\; d_{1}=0,\; z=y. \] \[ ||D_{BL}(\bar{y}-|w^{0}|)||_{2}\leq0\Longleftrightarrow ||A_{2}^{\top}z+C_{2}||_{2}\leq b^{\top}_{2}z+d_{2}\\ A_{2}^{\top}=D_{BL},\; C_{2}=-D_{BL}\times |w^{0}|,\; b_{2}=0_{n\times 1},\; d_{2}=0,\; z=\bar{y}. \] \[ ||D_{BL}\bar{x}||_{2}\leq0\Longleftrightarrow ||A_{3}^{\top}z+C_{3}||_{2}\leq b^{\top}_{3}z+d_{3}\\ A_{3}^{\top}=D_{BL},\; C_{3}=0,\; b_{3}=0_{n\times 1},\; d_{3}=0,\; z=\bar{x}. \]
    See Also:
    "Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."
    • Constructor Detail

      • SOCPNoTradingList2

        public SOCPNoTradingList2​(Vector w_0,
                                  Matrix D_BL0,
                                  double epsilon)
        Constructs a black list constraint.
        Parameters:
        w_0 - the initial position
        D_BL0 - the black list matrix
        epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
      • SOCPNoTradingList2

        public SOCPNoTradingList2​(Vector w_0,
                                  Matrix D_BL0)
        Constructs a black list constraint.
        Parameters:
        w_0 - the initial position
        D_BL0 - the black list matrix
    • Method Detail

      • evaluate

        public Double evaluate​(Vector x)
        Note: x here is the trading size, not the position. Evaluate the function f at x, where x is from the domain.
        Parameters:
        x - trading size
        Returns:
        constraint value
      • 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