## Working with Linear Inequality Constraints Using PortfolioCVaR Object

Linear inequality constraints are optional linear constraints that impose systems of
inequalities on portfolio weights (see Linear Inequality Constraints). Linear inequality constraints have
properties `AInequality`

for the inequality constraint matrix,
and` bInequality`

for the inequality constraint vector.

### Setting Linear Inequality Constraints Using the `PortfolioCVaR`

Function

The properties for linear inequality constraints are set using the `PortfolioCVaR`

object. Suppose that
you have a portfolio of five assets and you want to ensure that the first three
assets are no more than 50% of your portfolio. To set up these
constraints:

A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioCVaR('AInequality', A, 'bInequality', b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0.5000

### Setting Linear Inequality Constraints Using the `setInequality`

and `addInequality`

Functions

You can also set the properties for linear inequality constraints using `setInequality`

. Suppose that you
have a portfolio of five assets and you want to ensure that the first three assets
constitute no more than 50% of your portfolio. Given a
`PortfolioCVaR`

object `p`

, use `setInequality`

to set the linear
inequality constraints:

A = [ 1 1 1 0 0 ]; b = 0.5; p = PortfolioCVaR; p = setInequality(p, A, b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0.5000

Suppose that you want to add another linear inequality constraint to ensure that
the last three assets constitute at least 50% of your portfolio. You can set up an
augmented system of linear inequalities or use the `addInequality`

function to build up
linear inequality constraints. For this example, create another system of
inequalities:

p = PortfolioCVaR; A = [ 1 1 1 0 0 ]; % first inequality constraint b = 0.5; p = setInequality(p, A, b); A = [ 0 0 -1 -1 -1 ]; % second inequality constraint b = -0.5; p = addInequality(p, A, b); disp(p.NumAssets) disp(p.AInequality) disp(p.bInequality)

5 1 1 1 0 0 0 0 -1 -1 -1 0.5000 -0.5000

The `PortfolioCVaR`

object, `setInequality`

, and `addInequality`

implement scalar
expansion on the `bInequality`

property based on the dimension of
the matrix in the `AInequality`

property.

## See Also

`PortfolioCVaR`

| `setDefaultConstraints`

| `setBounds`

| `setBudget`

| `setGroups`

| `setGroupRatio`

| `setEquality`

| `setInequality`

| `setTurnover`

| `setOneWayTurnover`

## Related Examples

- Creating the PortfolioCVaR Object
- Working with CVaR Portfolio Constraints Using Defaults
- Validate the CVaR Portfolio Problem
- Estimate Efficient Portfolios for Entire Frontier for PortfolioCVaR Object
- Estimate Efficient Frontiers for PortfolioCVaR Object
- Asset Returns and Scenarios Using PortfolioCVaR Object
- Hedging Using CVaR Portfolio Optimization
- Compute Maximum Reward-to-Risk Ratio for CVaR Portfolio