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

Class SOCPSectorExposure

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

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

  • Constructor Details

    • SOCPSectorExposure

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

    • SOCPSectorExposure

      public SOCPSectorExposure(Vector w_0, Vector[] S, Vector u)
      Constructs a sector exposure constraint.
      Parameters:
      w_0 - the initial position
      S - the sector indicators
      u - the sector exposures

  • 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 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