Package tech.nmfin.portfoliooptimization.socp.constraints

Class SOCPZeroValue

java.lang.Object
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint
tech.nmfin.portfoliooptimization.socp.constraints.SOCPZeroValue
All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction
public class SOCPZeroValue extends SOCPPortfolioConstraint
Transforms a zero value constraint into the compact SOCP form.

The zero value constraint is: \[ \sum_{j=1}^{n}(w_{j}^{0}+x_{j})=0. \] By letting \(y=x+w^{0}\), the zero value constraint can be written as: \[ e^{\top}y=0, \] where \(e\in\mathbb{R}^{n}=(1,\cdots,1)^{\top}\). And it is equivalent to: \[ ||e^{\top}y||_{2}\leq 0. \] As a result the standard SOCP form of the zero value constraint can be written as: \[ ||e^{\top}y||_{2}\leq 0\Longleftrightarrow ||A^{\top}z+C||_{2}\leq b^{\top}z+d\\ A^{\top}=e^{\top},\; C=0,\; b=0_{n\times 1},\; d=0,\; z=y. \]
See Also:
  • "Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."

  • Constructor Details

    • SOCPZeroValue

      public SOCPZeroValue(Vector w_0, double epsilon)
      Constructs a zero value constraint.
      Parameters:
      w_0 - the initial position
      epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

    • SOCPZeroValue

      public SOCPZeroValue(Vector w_0)
      Constructs a zero value constraint.
      Parameters:
      w_0 - the initial position

  • Method Details

    • bias

      public double bias(Vector y)
      Computes the amount of deviation from zero value, hence bias.
      Parameters:
      y - the positions
      Returns:
      the sector bias

    • 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 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