Package tech.nmfin.portfoliooptimization.socp.constraints

Class SOCPMaximumLoan

java.lang.Object
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint
tech.nmfin.portfoliooptimization.socp.constraints.SOCPMaximumLoan
All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction
public class SOCPMaximumLoan extends SOCPPortfolioConstraint
Transforms a maximum loan constraint into the compact SOCP form. The maximum loan constraint is: \[ x_j+\max(0,w_j^0)\geq l_j,\quad l_j\leq 0,\quad j=1,\ldots,n. \] By letting \(y=x+w^{0}\), the maximum loan constraints are changed to: \[ y_j-w_{j}^{0}+\max(0,w_j^0)\geq l_j,\quad l_j\leq 0,\quad j=1,\ldots,n. \] Because \(\max(0,w_j^0)\Longleftrightarrow \frac{|w_j^0|+w_j^0}{2}\), we have \[ ||0||_{2}\leq y_{j}+\frac{|w_j^0|-w_j^0}{2}-l_{j},\quad l_j\leq 0,\quad j=1,\ldots,n. \] And the above constraints can be transformed into the standard SOCP form: \[ ||0||_{2}\leq y_{j}+\frac{|w_j^0|-w_j^0}{2}-l_{j}\Longleftrightarrow ||A_{j}^{\top}z+C_{j}||_{2}\leq b^{\top}_{j}z+d_{j},\quad j=1,\cdots,n\\ A_{j}^{\top}=0_{1\times n},\; C_{j}=0,\; b_{j}=e_{j},\; d_{j}=\frac{|w_j^0|-w_j^0}{2}-l_{j},\; z=y, \] where \(e_{j}\) is a \(n\) dimensional vector whose \(j\)th entry is \(1\) and the rest entries are \(0\).
See Also:
  • "Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."

  • Constructor Details

    • SOCPMaximumLoan

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

    • SOCPMaximumLoan

      public SOCPMaximumLoan(Vector w_0, Vector l)
      Constructs a maximum loan constraint.
      Parameters:
      w_0 - the initial position
      l - the maximum loan

  • 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