# Class SOCPSectorNeutrality

All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction

public class SOCPSectorNeutrality extends SOCPPortfolioConstraint
Transforms a sector neutral constraint into the compact SOCP form.

The sector neutral constraint is: $\sum_{j\in S_i}(w_j^0+x_j)=0,\quad i=1,\ldots,k,$ where $$S_i$$ is the $$i$$th section indicator. By letting $$y=x+w^{0}$$, the sector neutral constraint can be written as: $\sum_{j\in S_i}y_{j}=0, i=1,\cdots,k.$ And it is equivalent to: $||(\sum_{j\in S_{i}}e_{j})^{\top}y||_{2}\leq 0.$ As a result the standard SOCP form of the sector neutral constraint can be written as: $||(\sum_{j\in S_{i}}e_{j})^{\top}y||_{2}\leq 0\Longleftrightarrow ||A_{i}^{\top}z+C_{i}||_{2}\leq b^{\top}_{i}z+d_{i},\quad i=1,\cdots,k\\ A_{i}^{\top}=\sum_{j\in S_{i}}e^{\top}_{j},\; C_{i}=0,\; b_{i}=0_{n\times 1},\; d_{i}=0,\; z=y.$
• "Reformulate the Portfolio Optimization Problem as a Second Order Cone Programming Problem, Version 7."

## Nested classes/interfaces inherited from class dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint

SOCPPortfolioConstraint.ConstraintViolationException, SOCPPortfolioConstraint.Variable

## Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException
• ## Constructor Summary

Constructors
Constructor
Description
SOCPSectorNeutrality(Vector w_0, Vector[] S)
Constructs a sector neutral constraint.
SOCPSectorNeutrality(Vector w_0, Vector[] S, double epsilon)
Constructs a sector neutral constraint.
• ## Method Summary

Modifier and Type
Method
Description
boolean
areAllConstraintsSatisfied(Vector y)
Checks whether all SOCP constraints represented by this portfolio constraint are satisfied.
double
bias(Vector y)
Computes the amount of deviation from neutrality, 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 dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint

generalConstraints, getVariables, linearEqualities, linearInequalities, newSOCPGeneralConstraints, newSOCPLinearEqualities, newSOCPLinearInequalities

### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ## Constructor Details

• ### SOCPSectorNeutrality

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

public SOCPSectorNeutrality(Vector w_0, Vector[] S)
Constructs a sector neutral constraint.
Parameters:
w_0 - the initial position
S - the sector indicators
• ## Method Details

• ### bias

public double bias(Vector y)
Computes the amount of deviation from neutrality, 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