Package tech.nmfin.portfoliooptimization.socp.constraints.ybar

Class SOCPNoTradingList2

java.lang.Object
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint
tech.nmfin.portfoliooptimization.socp.constraints.ybar.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 Details

    • 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 Details

    • areAllConstraintsSatisfied

      public boolean areAllConstraintsSatisfied(Vector y) throws SOCPPortfolioConstraint.ConstraintViolationException
      Description copied from class: SOCPPortfolioConstraint
      Checks whether all SOCP constraints represented by this portfolio constraint are satisfied.
      Specified by:
      areAllConstraintsSatisfied in class SOCPPortfolioConstraint
      Parameters:
      y - a portfolio solution or allocation; the asset weights
      Returns:
      true if and only if all SOCP constraints are satisfied
      Throws:
      SOCPPortfolioConstraint.ConstraintViolationException

    • 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