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

Transforms a black list (not to trade a new position) constraint into the compact SOCP form.

The black list constraint is: $x_{j}=0,$ for j in the black list. By letting $$y=x+w^{0}$$,$$\bar{y}=|x+w^{0}|$$ and $$\bar{x}=|x|$$, the black list constraints are changed to: $y_{j}=w^{0}_{j},\;\bar{y}_{j}=|w^{0}_{j}|,\;\bar{x}_{j}=0,$ for j in the black list. Denote the black list index set as $$BL$$, i.e. $$BL=\{j|x_{j}=0\}$$. As $$y_{j}=x_{j}+w_{j}^{0}$$, the set $$BL$$ can be written as $$BL=\{j|y_{j}=w_{j}^{0}\}$$. The black list constraints can be written in the following form: $||D_{BL}(y-w^{0})||_{2}\leq0,\;||D_{BL}(\bar{y}-|w^{0}|)||_{2}\leq0,\;||D_{BL}\bar{x}||_{2}\leq0,$ where $$D_{BL}$$ is a diagonal matrix. The $$k$$th diagonal entry of $$D_{BL}$$, $$D_{BL}(k,k)$$, is $$1$$ if $$k\in BL$$, otherwise it is $$0$$. These constraints can be transformed into the standard SOCP form: $||D_{BL}(y-w^{0})||_{2}\leq0\Longleftrightarrow ||A_{1}^{\top}z+C_{1}||_{2}\leq b^{\top}_{1}z+d_{1}\\ A_{1}^{\top}=D_{BL},\; C_{1}=-D_{BL}\times w^{0},\; b_{1}=0_{n\times 1},\; d_{1}=0,\; z=y.$ $||D_{BL}(\bar{y}-|w^{0}|)||_{2}\leq0\Longleftrightarrow ||A_{2}^{\top}z+C_{2}||_{2}\leq b^{\top}_{2}z+d_{2}\\ A_{2}^{\top}=D_{BL},\; C_{2}=-D_{BL}\times |w^{0}|,\; b_{2}=0_{n\times 1},\; d_{2}=0,\; z=\bar{y}.$ $||D_{BL}\bar{x}||_{2}\leq0\Longleftrightarrow ||A_{3}^{\top}z+C_{3}||_{2}\leq b^{\top}_{3}z+d_{3}\\ A_{3}^{\top}=D_{BL},\; C_{3}=0,\; b_{3}=0_{n\times 1},\; d_{3}=0,\; z=\bar{x}.$
• "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
SOCPNoTradingList2(Vector w_0, Matrix D_BL0)
Constructs a black list constraint.
SOCPNoTradingList2(Vector w_0, Matrix D_BL0, double epsilon)
Constructs a black list constraint.
• ## Method Summary

Modifier and Type
Method
Description
boolean
areAllConstraintsSatisfied(Vector y)
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 x)
Note: x here is the trading size, not the position. 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

public SOCPNoTradingList2(Vector w_0, Matrix D_BL0, double epsilon)
Constructs a black list constraint.
Parameters:
w_0 - the initial position
D_BL0 - the black list matrix
epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Constructs a black list constraint.
Parameters:
w_0 - the initial position
D_BL0 - the black list matrix
• ## 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 x)
Note: x here is the trading size, not the position. Evaluate the function f at x, where x is from the domain.
Parameters:
x - trading size
Returns:
constraint value
• ### 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