# SuanShu, a Java numerical and statistical library

## Class SOCPZeroValue

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

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: $||e^{\top}y||_{2}\leq 0\Longleftrightarrow ||A^{\top}z+C||_{2}\leq b^{\top}z+d\\ A^{\top}=e^{\top},\; C=0,\; b=0_{n\times 1},\; d=0,\; z=y.$
"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
SOCPZeroValue(Vector w_0)
Constructs a zero value constraint.
SOCPZeroValue(Vector w_0, double epsilon)
Constructs a zero value 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.
double bias(Vector y)
Computes the amount of deviation from zero value, hence bias.
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

• #### 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 Detail

• #### 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 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