# Documentation

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Add linear inequality constraints for portfolio weights to existing constraints

Use the `addInequality` function with a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object to add linear inequality constraints for portfolio weights to existing constraints.

For details on the respective workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

## Syntax

``obj = addInequality(obj,AInequality,bInequality)``

## Description

example

````obj = addInequality(obj,AInequality,bInequality)` adds linear inequality constraints for portfolio weights to existing constraints.Given a linear inequality constraint matrix `AInequality` and vector `bInequality`, every weight in a portfolio `Port` must satisfy the following:AInequality * Port = bInequalityThis function "stacks" additional linear inequality constraints onto any existing linear inequality constraints that exist in the input portfolio object. If no constraints exist, this function is the same as `setInequality`.```

## Examples

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Set a linear inequality constraint to ensure that the first three assets constitute at most 50% of a portfolio. Then add another linear inequality constraint to ensure that the last three assets constitute at least 50% of a portfolio.

```p = Portfolio; 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);```
``` 5 ```
`disp(p.AInequality);`
``` 1 1 1 0 0 0 0 -1 -1 -1 ```
`disp(p.bInequality);`
``` 0.5000 -0.5000 ```

Set a linear inequality constraint to ensure that the first three assets constitute at most 50% of a portfolio. Then add another linear inequality constraint to ensure that the last three assets constitute at least 50% of a portfolio.

```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);```
``` 5 ```
`disp(p.AInequality);`
``` 1 1 1 0 0 0 0 -1 -1 -1 ```
`disp(p.bInequality);`
``` 0.5000 -0.5000 ```

Set a linear inequality constraint to ensure that the first three assets constitute at most 50% of a portfolio. Then add another linear inequality constraint to ensure that the last three assets constitute at least 50% of a portfolio.

```p = PortfolioMAD; 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);```
``` 5 ```
`disp(p.AInequality);`
``` 1 1 1 0 0 0 0 -1 -1 -1 ```
`disp(p.bInequality);`
``` 0.5000 -0.5000 ```

## Input Arguments

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Object for portfolio, specified using `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object. For more information on creating a portfolio object, see

Linear inequality constraints, specified as a matrix.

### Note

An error results if `AInequality` is empty and `bInequality` is nonempty.

Data Types: `double`

Linear inequality constraints, specified as a vector.

### Note

An error results if `bInequality` is empty and `AInequality` is nonempty.

Data Types: `double`

## Output Arguments

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Updated portfolio object, returned as a `Portfolio`, `PortfolioCVaR`, or `PortfolioMAD` object. For more information on creating a portfolio object, see

## Tips

• You can also use dot notation to add the linear inequality constraints for portfolio weights.

`obj = obj.addInequality(AInequality, bInequality)`

• You can also remove linear inequality constraints from any of the portfolio objects using dot notation.

`obj = obj.setInequality([ ], [ ])`