tech.nmfin.portfoliooptimization.socp.constraints

Class SOCPZeroValue

java.lang.Object

dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint

tech.nmfin.portfoliooptimization.socp.constraints.SOCPZeroValue

All Implemented Interfaces:

Function<Vector,Double>, RealScalarFunction

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: \[ ||e^{\top}y||_{2}\leq 0\Longleftrightarrow ||A^{\top}z+C||_{2}\leq b^{\top}z+d\\ A^{\top}=e^{\top},\; C=0,\; b=0_{n\times 1},\; d=0,\; z=y. \]

See Also:

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

Nested Class Summary

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 and Description
SOCPZeroValue(Vector w_0) Constructs a zero value constraint.
SOCPZeroValue(Vector w_0, double epsilon) Constructs a zero value constraint.

Method Summary

Modifier and Type	Method and 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 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 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 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 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 \(R^{n}\to R^{m}\) function, the dimension of the range is m.

Returns:

the dimension of the range