# SuanShu, a Java numerical and statistical library

## Class SOCPMaximumLoan

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

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 $$0$$.
"Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."

• ### Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint

SOCPPortfolioConstraint.ConstraintViolationException, SOCPPortfolioConstraint.Variable
• ### Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException
• ### Constructor Summary

Constructors
Constructor and Description
SOCPMaximumLoan(Vector w_0, Vector l)
Constructs a maximum loan constraint.
SOCPMaximumLoan(Vector w_0, Vector l, double epsilon)
Constructs a maximum loan constraint.
• ### Method Summary

All Methods
Modifier and Type Method and Description
boolean areAllConstraintsSatisfied(Vector x)
Checks whether all SOCP constraints represented by this portfolio constraint are satisfied.
int dimensionOfDomain()
Get the number of variables the function has.
int dimensionOfRange()
Get the dimension of the range space of the function.
Double evaluate(Vector y)
Evaluate the function f at x, where x is from the domain.
• ### Methods inherited from class com.numericalmethod.suanshu.optimization.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint

getVariables, iterator, newSOCPGeneralConstraints
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface java.lang.Iterable

forEach, spliterator
• ### Constructor Detail

• #### 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 Detail

• #### areAllConstraintsSatisfied

public boolean areAllConstraintsSatisfied(Vector x)
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:
x - 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